I just searched the message board and couldn't find any threads that list the games that appeared on the cover of each issue of Nintendo Power, so here it is. This list was compiled from several web sites:
Nintendo Power Index on Retromags.com
List of Nintendo Power Covers from TheConsoler.com (Google cache)
Read-a-long with Nintendo Power on Aeropause.com
Nintendo Fun Club News on Tomheroes.com
Nintendo Power Index - 1987 & 1988 on Retromags.com (Google cache)
Nintendo: The Good, the Bad, and the Ugly on I-Mockery.com
Also, thanks to fellow DP members Darkhades, Lendelin, and especially Namzep and Gameboy Color/JSoup for continually posting the latest issues!
1987:
Nintendo Fun Club News Vol. 1 #1 (winter 1987): Super Mario Bros.
Nintendo Fun Club News Vol. 1 #2 (summer 1987): The Legend of Zelda
Nintendo Fun Club News Vol. 1 #3 (fall 1987): The Legend of Zelda
Nintendo Fun Club News Vol. 1 #4 (winter 1987): Mike Tyson's Punch-Out!!
1988:
Nintendo Fun Club News Vol. 1 #5 (February/March 1988): R.C. Pro-Am
Nintendo Fun Club News Vol. 2 #6 (April/May 1988): Zelda II: The Adventure of Link
Nintendo Fun Club News Vol. 2 #7 (June/July 1988): Sports '88 Wrap Up
Nintendo Power (001) (July/August 1988): Super Mario Bros. 2
Nintendo Power (002) (September/October 1988): Castlevania II: Simon's Quest
Nintendo Power (003) (November/December 1988): Track & Field II
1989:
Nintendo Power (004) (January/February 1989): Zelda II: The Adventure of Link
Nintendo Power (005) (March/April 1989): Ninja Gaiden
Nintendo Power (006) (May/June 1989): Teenage Mutant Ninja Turtles
Nintendo Power (007) (July/August 1989): Mega Man II
Nintendo Power (008) (September/October 1989): DuckTales
Nintendo Power (009) (November/December 1989): Tetris
1990:
Nintendo Power (010) (January/February 1990): Batman (first Nintendo Power cover to feature a celebrity - Jack Nicholson as The Joker)
Nintendo Power (011) (March/April 1990): Super Mario Bros. 3
Nintendo Power (012) (May/June 1990): Super C
Nintendo Power 013 (no date): Super Mario Bros. 3 strategy guide (first full-length Nintendo Power strategy guide, first issue to be numbered)
Nintendo Power (014) (July/August 1990): Chip 'n Dale Rescue Rangers
Nintendo Power 015 (no date): Ninja Gaiden II strategy guide
Nintendo Power 016 (September/October 1990): Maniac Mansion (first regular issue to be numbered)
Nintendo Power 017 (no date): Final Fantasy strategy guide
Nintendo Power 018 (November/December 1990): Dr. Mario
Nintendo Power 019 (no date): 4-Player Extra strategy guide (last NP strategy guide to be counted as a sequential issue)
1991:
Nintendo Power 020 (January 1991): Mega Man III
Nintendo Power 021 (February 1991): StarTropics
Nintendo Power 022 (March 1991): Metal Storm
Nintendo Power 023 (April 1991): Power Blade
Nintendo Power 024 (May 1991): Vice: Project Doom
Nintendo Power 025 (June 1991): Battletoads
Nintendo Power 026 (July 1991): Robin Hood: Prince of Thieves
Nintendo Power 027 (August 1991): Mega Man in Dr. Wily's Revenge (first cover to feature a Game Boy game)
Nintendo Power 028 (September 1991): Super Mario World (first cover to feature an SNES game)
Nintendo Power 029 (October 1991): Star Trek
Nintendo Power 030 (November 1991): Final Fantasy II (U.S.)
Nintendo Power 031 (December 1991): Metroid II: Return of Samus
1992:
Nintendo Power 032 (January 1992): Super Castlevania IV
Nintendo Power 033 (February 1992): Teenage Mutant Ninja Turtles III: The Manhattan Project
Nintendo Power 034 (March 1992): The Legend of Zelda: A Link to the Past
Nintendo Power 035 (April 1992): WWF Super Wrestlemania (first Nintendo Power cover to feature a sports figure - Hulk Hogan)
Nintendo Power 036 (May 1992): Darkwing Duck
Nintendo Power 037 (June 1992): Lemmings
Nintendo Power 038 (July 1992): Street Fighter II: The World Warrior
Nintendo Power 039 (August 1992): Mario Paint
Nintendo Power 040 (September 1992): Felix the Cat
Nintendo Power 041 (October 1992): Super Mario Kart
Nintendo Power 042 (November 1992): Super Star Wars
Nintendo Power 043 (December 1992): Road Runner's Death Valley Rally
1993:
Nintendo Power 044 (January 1993): Magical Quest Starring Mickey Mouse
Nintendo Power 045 (February 1993): The Addams Family: Pugsley's Scavenger Hunt
Nintendo Power 046 (March 1993): Tiny Toon Adventures: Buster Busts Loose
Nintendo Power 047 (April 1993): Star Fox
Nintendo Power 048 (May 1993): Batman Returns
Nintendo Power 049 (June 1993): Battletoads & Double Dragon (last cover to feature an NES game)
Nintendo Power 050 (July 1993): The Legend of Zelda: Link's Awakening
Nintendo Power 051 (August 1993): Street Fighter II Turbo
Nintendo Power 052 (September 1993): Super Mario All-Stars
Nintendo Power 053 (October 1993): Super Empire Strikes Back
Nintendo Power 054 (November 1993): Secret of Mana
Nintendo Power 055 (December 1993): Aladdin
1994:
Nintendo Power 056 (January 1994): Mega Man X
Nintendo Power 057 (February 1994): Bugs Bunny Rabbit Rampage
Nintendo Power 058 (March 1994): Wario Land: Super Mario Land 3
Nintendo Power 059 (April 1994): Ken Griffey Jr. Presents Major League Baseball
Nintendo Power 060 (May 1994): Super Metroid
Nintendo Power 061 (June 1994): Donkey Kong (first cover to feature a Super Game Boy game)
Nintendo Power 062 (July 1994): Super Street Fighter II
Nintendo Power 063 (August 1994): Stunt Race FX
Nintendo Power 064 (September 1994): Mortal Kombat II
Nintendo Power 065 (October 1994): Illusion of Gaia
Nintendo Power 066 (November 1994): Donkey Kong Country (first cover to feature 3D computer rendered art)
Nintendo Power 067 (December 1994): Earthworm Jim
1995:
Nintendo Power 068 (January 1995): The Adventures of Batman and Robin (first issue to feature the new 3D computer rendered logo)
Nintendo Power 069 (February 1995): Mega Man X2
Nintendo Power 070 (March 1995): NBA Jam Tournament Edition
Nintendo Power 071 (April 1995): Stargate
Nintendo Power 072 (May 1995): Kirby's Dream Land 2
Nintendo Power 073 (June 1995): Weaponlord
Nintendo Power 074 (July 1995): Donkey Kong Land
Nintendo Power 075 (August 1995): Virtual Boy debut (only cover to feature the Virtual Boy)
Nintendo Power 076 (September 1995): Killer Instinct
Nintendo Power 077 (October 1995): Super Mario World 2: Yoshi's Island
Nintendo Power 078 (November 1995): Mortal Kombat 3
Nintendo Power 079 (December 1995): Donkey Kong Country 2: Diddy's Kong Quest
1996:
Nintendo Power 080 (January 1996): Happy NU64 Year (New Year Celebration cover)
Nintendo Power 081 (February 1996): Killer Instinct 2
Nintendo Power 082 (March 1996): Super Mario RPG: Legend of the Seven Stars
Nintendo Power 083 (April 1996): Earthworm Jim 2
Nintendo Power 084 (May 1996): Ken Griffey, Jr.'s Winning Run
Nintendo Power 085 (June 1996): Super Mario 64 (first cover to feature a Nintendo 64 game)
Nintendo Power 086 (July 1996): E3 1996
Nintendo Power 087 (August 1996): Tetris Attack
Nintendo Power 088 (September 1996): Super Mario 64
Nintendo Power 089 (October 1996): Mortal Kombat Trilogy
Nintendo Power 090 (November 1996): Donkey Kong Country 3: Dixie Kong's Double Trouble! (last cover to feature an SNES game)
Nintendo Power 091 (December 1996): Killer Instinct Gold
1997:
Nintendo Power 092 (January 1997): Star Wars: Shadows of the Empire (4 different covers)
Nintendo Power 093 (February 1997): Mario Kart 64
Nintendo Power 094 (March 1997): Turok: Dinosaur Hunter
Nintendo Power 095 (April 1997): Blast Corps
Nintendo Power 096 (May 1997): Doom 64
Nintendo Power 097 (June 1997): Clayfighter 63 1/3
Nintendo Power 098 (July 1997): Star Fox 64
Nintendo Power 099 (August 1997): GoldenEye 007
Nintendo Power 100 (September 1997): 100th Issue Anniversary
Nintendo Power 101 (October 1997): Extreme-G
Nintendo Power 102 (November 1997): NFL Quarterback Club '98
Nintendo Power 103 (December 1997): Diddy Kong Racing
1998:
Nintendo Power 104 (January 1998): Yoshi's Story
Nintendo Power 105 (February 1998): WCW Vs. NWO: World Tour
Nintendo Power 106 (March 1998): 1080° Snowboarding
Nintendo Power 107 (April 1998): Kobe Bryant in NBA Courtside
Nintendo Power 108 (May 1998): MLB Featuring Ken Griffey, Jr.
Nintendo Power 109 (June 1998): Banjo-Kazooie
Nintendo Power 110 (July 1998): WWF: War Zone
Nintendo Power 111 (August 1998): Bomberman Hero
Nintendo Power 112 (September 1998): F-Zero X
Nintendo Power 113 (October 1998): Turok 2: Seeds of Evil
Nintendo Power 114 (November 1998): The Legend of Zelda: Ocarina of Time (Nintendo Power's largest issue to date)
Nintendo Power 115 (December 1998): Star Wars: Rogue Squadron
1999:
Nintendo Power 116 (January 1999): Castlevania
Nintendo Power 117 (February 1999): Mario Party
Nintendo Power 118 (March 1999): Tonic Trouble
Nintendo Power 119 (April 1999): Beetle Adventure Racing
Nintendo Power 120 (May 1999): Star Wars: Episode I Racer
Nintendo Power 121 (June 1999): Pokemon Snap
Nintendo Power 122 (July 1999): World Driver: Championship
Nintendo Power 123 (August 1999): Hybrid Heaven
Nintendo Power 124 (September 1999): Jet Force Gemini
Nintendo Power 125 (October 1999): Pokemon Yellow
Nintendo Power 126 (November 1999): Donkey Kong 64
Nintendo Power 127 (December 1999): WWF Wrestlemania 2000
2000:
Nintendo Power 128 (January 2000): Mario Party 2
Nintendo Power 129 (February 2000): Tarzan
Nintendo Power 130 (March 2000): Pokemon Stadium
Nintendo Power 131 (April 2000): Tony Hawk's Pro Skater
Nintendo Power 132 (May 2000): Excitebike 64
Nintendo Power 133 (June 2000): Army Men: Air Combat
Nintendo Power 134 (July 2000): Kirby 64: The Crystal Shards
Nintendo Power 135 (August 2000): Mario Tennis
Nintendo Power 136 (September 2000): Pokemon Gold/ Pokemon Silver
Nintendo Power 137 (October 2000): The Legend of Zelda: Majora's Mask
Nintendo Power 138 (November 2000): Hey You, Pikachu!
Nintendo Power 139 (December 2000): Banjo-Tooie
2001:
Nintendo Power 140 (January 2001): Spider-Man
Nintendo Power 141 (February 2001): Paper Mario
Nintendo Power 142 (March 2001): Pokemon Stadium 2
Nintendo Power 143 (April 2001): Game Boy Advance (first cover to feature the white Nintendo Power logo)
Nintendo Power 144 (May 2001): The Legend of Zelda: Oracle of Ages/The Legend of Zelda: Oracle of Seasons
Nintendo Power 145 (June 2001) Super Mario Advance (first cover to feature a Game Boy Advance game)
Nintendo Power 146 (July 2001): Tony Hawk's Pro Skater 2 (last cover to feature a Nintendo 64 game)
Nintendo Power 147 (August 2001): Pokemon Crystal
Nintendo Power 148 (September 2001): Mario Kart Super Circuit
Nintendo Power 149 (October 2001): Star Wars: Rogue Squadron II: Rogue Leader (first cover to feature a GameCube game)
Nintendo Power 150 (November 2001): It's Here! (Luigi's Mansion)
Nintendo Power 151 (December 2001): Super Smash Bros. Melee
Nintendo Power Advance v.1 (2001): Super Mario Advance
Nintendo Power Advance v.2 (2001): Mario Kart: Super Circuit
Nintendo Power Advance v.3 (2001): Golden Sun
2002:
Nintendo Power 152 (January 2002): Pikmin
Nintendo Power 153 (February 2002): NBA Courtside 2002
Nintendo Power 154 (March 2002): Sonic Adventure 2: Battle (first cover for a Sega game)
Nintendo Power 155 (April 2002): Agent Under Fire
Nintendo Power 156 (May 2002): Spider-Man
Nintendo Power 157 (June 2002): Lost Kingdoms
Nintendo Power 158 (July 2002): E3 2002
Nintendo Power 159 (August 2002): Magical Mirror starring Mickey Mouse
Nintendo Power 160 (September 2002): Super Mario Sunshine
Nintendo Power 161 (October 2002): Star Fox Adventures
Nintendo Power 162 (November 2002): Metroid Prime
Nintendo Power 163 (December 2002): Metroid Fusion (first cover to feature a side-panel featuring other titles)
Nintendo Power Advance v.4 (2002): Super Mario World: Super Mario Advance 2
2003:
Nintendo Power 164 (January 2003): The Lord of the Rings: The Two Towers
Nintendo Power 165 (February 2003): The Legend of Zelda: The Wind Waker
Nintendo Power 166 (March 2003): The Sims
Nintendo Power 167 (April 2003): Pokemon Ruby/Pokemon Sapphire
Nintendo Power 168 (May 2003): Golden Sun: The Lost Age
Nintendo Power 169 (June 2003): Soul Calibur 2
Nintendo Power 170 (July/August 2003): F-Zero GX
Nintendo Power 171 (September 2003): Final Fantasy Tactics Advance
Nintendo Power 172 (October 2003): Viewtiful Joe
Nintendo Power 173 (November 2003): Star Wars: Rogue Squadron III: Rebel Strike
Nintendo Power 174 (December 2003): Fire Emblem
2004:
Nintendo Power 175 (January 2004): Mario Kart: Double Dash!!
Nintendo Power 176 (February 2004): The Sims: Bustin' Out
Nintendo Power 177 (March 2004): Final Fantasy: Crystal Chronicles (4 different covers)
Nintendo Power 178 (April 2004): Pokemon Colosseum
Nintendo Power 179 (May 2004): Metal Gear Solid: The Twin Snakes
Nintendo Power 180 (June 2004): Tales of Symphonia
Nintendo Power 181 (July 2004): The Legend of Zelda: Four Swords Adventures
Nintendo Power 182 (August 2004): Resident Evil 4
Nintendo Power 183 (September 2004): Pikmin 2
Nintendo Power 184 (October 2004): Pokemon FireRed/Pokemon LeafGreen
Nintendo Power 185 (November 2004): Paper Mario: The Thousand-Year Door
Nintendo Power 186 (December 2004): Metroid Prime 2: Echoes
2005:
Nintendo Power 187 (January 2005): Nintendo DS
Nintendo Power 188 (February 2005): The Legend of Zelda: The Minish Cap
Nintendo Power 189 (March 2005): Star Fox: Assault (last cover to feature the side-panel)
Nintendo Power 190 (April 2005): Killer 7
Nintendo Power 191 (May 2005): Nintendo DS (including Metroid Prime Hunters)
Nintendo Power 192 (June 2005): Pokemon Emerald (first issue with glossy cover)
Nintendo Power 193 (July 2005): The Legend of Zelda: Twilight Princess (first cover to feature the major redesign, including the new Nintendo Power logo)
Nintendo Power 194 (August 2005): Ready for Wi-fi (Mario Kart DS) (first cover to feature a Nintendo DS game)
Nintendo Power 195 (September 2005): Hog Heaven (Shadow the Hedgehog)
Nintendo Power 196 (October 2005): Play with Fire (Harry Potter and the Goblet of Fire)
Nintendo Power 197 (November 2005): The XD Factor (Pokemon XD: Gale of Darkness)
Nintendo Power 198 (December 2005): Class Warfare (Fire Emblem: Path of Radiance)
2006:
Nintendo Power 199 (January 2006): Nintendo Wi-Fi Connection (Mario Kart DS, Animal Crossing: Wild World, Tony Hawk: American Sk8land)
Nintendo Power 200 (February 2006): Touch Evil! (Resident Evil: Deadly Silence)
Nintendo Power 201 (March 2006): Gonzo Gaming! (Chibi-Robo)
Nintendo Power 202 (April 2006): Alien Seduction? (Metroid Prime Hunters)
Nintendo Power 203 (May 2006): Jump for Joy! (New Super Mario Bros.)
Nintendo Power 204 (June 2006): Castlevania: Portrait of Ruin
Nintendo Power 205 (July 2006): Zelda (The Legend of Zelda: Phantom Hourglass)
Nintendo Power 206 (August 2006): We Came, Wii Conquered (E3 2006)
Nintendo Power 207 (September 2006): Bunnies Gone Bad (Rayman Raving Rabbids) (first cover to feature a Wii game. It can be argued that issue 193 featuring Twilight Princess is the first, but at the time of that issue's release, it had not officially been announced as a Wii title and was still set for GameCube only.)
Nintendo Power 208 (October 2006): Final Fantasy III
Nintendo Power 209 (November 2006): Let's Talk (Pokemon Mystery Dungeon) (last cover to feature a Game Boy Advance game)
Nintendo Power 210 (December 2006): Here We Go! (Wii Launch)
2007:
Nintendo Power 211 (January 2007): We Dream of Zelda (The Legend of Zelda: Twilight Princess) (last cover to feature a GameCube game)
Nintendo Power 212 (February 2007): Ready to 'Ware (WarioWare: Smooth Moves)
Nintendo Power 213 (March 2007): Sonic Secrets (Sonic and the Secret Rings)
Nintendo Power 214 (April 2007): Wii the Sims (My Sims)
Nintendo Power 215 (May 2007): Pokemon Perspectives (Pokemon Diamond and Pokemon Pearl)
Nintendo Power 216 (June 2007): Nights: Journey of Dreams
Nintendo Power 217 (July 2007): Resident Evils (Resident Evil: Umbrella Chronicles)
Nintendo Power 218 (August 2007): SoulCalibur Legends
Nintendo Power 219 (September 2007): Metroid's Primed (Metroid Prime 3: Corruption)
Nintendo Power 220 (October 2007): Far Out, Mario! (Super Mario Galaxy)
Nintendo Power 221 (November 2007): Final Fantasy XII: Revenant Wings
Nintendo Power 222 (December 2007): BRAWL! (Super Smash Bros. Brawl)
Nintendo Power 223 (holiday 2007): Wii Goes Punk (No More Heroes)
2008:
Nintendo Power 224 (January 2008): Ninja Gaiden: Dragon Sword
Nintendo Power 225 (February 2008): Sonic Chronicles: The Dark Brotherhood
Nintendo Power 226 (March 2008): Tales of Symphonia: Dawn of the New World
Nintendo Power 227 (April 2008): Mario Kart Wii
Nintendo Power 228 (May 2008): Final Fantasy IV
Nintendo Power 229 (June 2008): Music Games (Guitar Hero, Rock Band, and Samba de Amigo)
Nintendo Power 230 (July 2008): Castlevania: Order of Ecclesia (DS)
Nintendo Power Posters: A Supplement to Nintendo Power (40 posters)
Nintendo Power 231 (August 2008): MadWorld (Wii)
Nintendo Power 232 (September 2008): Sonic & the Black Knight (Wii)
Nintendo Power 233 (October 2008): Wario Land: Shake It! (Wii)
Nintendo Power 234 (November 2008): Grand Theft Auto: Chinatown Wars
Nintendo Power 235 (December 2008): Animal Crossing: City Folk
Nintendo Power 236 (Holiday 2008): Year-End Review Blowout
2009:
Nintendo Power 237 (January 2009): 2009 - The Year in Preview (TMNT cover)
Nintendo Power 238 (February 2009): RPG Special
Nintendo Power 239 (March 2009): Indiana Jones & the Staff of Kings
Nintendo Power 240 (April 2009) - Pokemon Platinum Version
Nintendo Power 241 (May 2009) - Silent Hill: Shattered Memories
Nintendo Power 242 (June 2009) - Red Steel 2
Nintendo Power 243 (July 2009) - Kingdom Hearts 358/2 Days
Nintendo Power 244 (August 2009) - Mario & Luigi: Bowser's Inside Story
Nintendo Power 245 (September 2009) - Final Fantasy Crystal Chronicles: The Crystal Bearers
Nintendo Power 246 (October 2009) - Avatar
Nintendo Power 247 (November 2009) - Mario & Sonic at the Olympic Winter Games
Nintendo Power 248 (December 2009) - New Super Mario Bros. Wii
Nintendo Power 249 (Holiday 2009) - The Legend of Zelda: Spirit Tracks
2010:
Nintendo Power 250 (January 2010) - 250 Reasons to Love Nintendo
Nintendo Power 251 (February 2010) - NBA Jam (Wii)
Nintendo Power 252 (March 2010) - Pokemon HeartGold/SoulSilver
Nintendo Power 253 (April 2010) - Scribblenauts 2
Nintendo Power 254 (May 2010) - Super Mario Galaxy 2
Nintendo Power 255 (June 2010) - Metroid: Other M
Nintendo Power 256 (July 2010) - Sonic Colors
Nintendo Power 257 (August 2010) - Dragon Quest IX: Sentinels of the Starry Skies
Nintendo Power 258 (September 2010) - The Legend of Zelda: Skyward Sword
Nintendo Power 259 (October 2010) - Epic Mickey
Nintendo Power 260 (November 2010) - Anniversary Special (25 years of NES)
Nintendo Power 261 (December 2010) - Donkey Kong Country Returns
Nintendo Power 262 (Holiday 2010) - Kingdom Hearts Re:coded
2011:
Nintendo Power 263 (January 2011) - Mario Sports Mix (Wii)
Nintendo Power 264 (February 2011) - Pokemon Black Version/Pokemon White Version
Nintendo Power 265 (March 2011) - 3DS Launch Special
Nintendo Power 266 (April 2011) - Pilotwings Resort (first cover to feature a 3DS game)
Nintendo Power 267 (May 2011) - The Legend of Zelda: Ocarina of Time 3D
Nintendo Power 268 (June 2011) - Sonic Generations
Nintendo Power 269 (July 2011) - Rayman Origins
Nintendo Power 270 (August 2011) - Star Fox 64 3D
Nintendo Power 271 (September 2011) - Kirby Mass Attack and Kirby's Return to Dream Land
Nintendo Power 272 (October 2011) - Super Mario 3D Land
Nintendo Power 273 (November 2011) - Mario Kart 7
Nintendo Power 274 (December 2011) - Holiday Special
2012:
Nintendo Power 275 (January/February 2012) - 2012 Preview Issue (Kid Icarus: Uprising)
Nintendo Power 276 (March 2012) - Kingdom Hearts 3D: Dream Drop Distance
Nintendo Power 277 (April 2012) - Epic Mickey 2: The Power of Two and Epic Mickey: Power of Illusion (last cover to feature a Wii game)
Nintendo Power 278 (May 2012) - Pokemon Conquest
Nintendo Power 279 (June 2012) - Castlevania: Lords of Shadow - Mirror of Fate
Nintendo Power 280 (July 2012) - Wii U (newsstand version)/Pikmin 3 (subscriber version, first cover to feature a Wii U game)
Nintendo Power 281 (August 2012) - Scribblenauts Unlimited
Nintendo Power 282 (September 2012) - Pokemon Black Version 2 and Pokemon White Version 2 (last cover to feature a DS game)
Nintendo Power 283 (October 2012) - Rayman Legends
Nintendo Power 284 (November 2012) - Wii U Prepare for Launch
Nintendo Power 285 (December 2012) - New Super Mario Bros. U (homage to the cover of Nintendo Power 1 from July/August 1988)
THE END