The SNES gets my vote, mainly because the Gamecube made me fall back in love with Nintendo. But, for the sake of making my reply interesting, I'll post my opinions on all 3.

SNES - Most well-rounded library of titles ever. Platformers? Both Super Mario Worlds and Mario All-Stars. Shooters? Gradius 3, Super R-Type, Space Megaforce. Character shooters? Contra 3, Mega Man X. Fighters? Street Fighter 2 (and SF2 Turbo), Mortal Kombat 2, even Art of Fighting! Beat 'em Ups? Super Double Dragon, Final Fight trilogy, TMNT 4. RPGs? FF2, FF3, Chrono Trigger, Secret of Mana, etc. Adventure games? Zelda 3, Super Metroid, Castlevania 4, Dracula X. Puzzle games? Tetris Attack, Tetris & Dr. Mario, Bust-a-Move.

Genesis - It takes good knowledge of late 80's and early 90's arcade games to really fully appreciate the Genesis. There are the obvious goodies, like Sonic, Streets of Rage, Gunstar Heroes, Columns, Phantasy Star, Shining Force and Toejam & Earl, but if you dig deeper, you have: Strider, Ghouls & Ghosts, Forgotten Worlds, Truxton, MUSHA, Golden Axe, the Shinobi trilogy, Valis III, Gaiares, Whip Rush, Arrow Flash, Rolling Thunder 2 & 3, Splatterhouse 2 & 3, Burning Force, Space Harrier 2, OutRun, Flicky, Phelios, Alex Kidd, Fire Shark, and more.

TurboGrafx-16 - Speaking of late 80's/early 90's arcade fare, that's almost all that you can get for this system! Certainly not a bad thing, though. I'll try and focus on U.S. titles....Bonk trilogy, Air Zonk, Ninja Spirit, Splatterhouse, Ordyne, Cyber-Core, Blazing Lazers, Aero Blasters, Galaga '90, Alien Crush & Devil's Crush. Of course, there were some real thinking games as well, such as Neutopia and Military Madness. You can also get Wonder Boy for the TG16! (As Dragon's Curse)