What do you look for in a new game? What makes a game memorable to you?

[Game Freak]

What do you all look for before buying a new game? I've mainly been only running on the "cheap factor"which usually lands me with some pretty bad NES, SNES, and Atari games, although at the store I go to they once gave me Sonic 2 for free, as well as Cosmic Ark, Out of This World, GunSmoke, and Golgo 13 for decent prices.

Also, what makes a game memorable? As a kid, I loved the Disney games my parents bought me. I still do to this day. The music is fantastic, the controls are easy, and the games do offer some difficulty. I mostly enjoy games for the music, which is why i have a good 60 hours or so of just video game music on my computer >_> mostly SNES titles. A list of my favorites for the SNES are below, and i love all their music :D

Addams Family, The*
Aladdin*
Animaniacs*
Beethoven*
Brunswick World Tournament of Champions*
Bubsy In: Clawed Encounters of the Furred Kind*
Championship Pool*
Donkey Kong Country*
Donkey Kong Country 2*
Final Fantasy: Mystic Quest
F-Zero
Izzy's Quest for the Olympic Rings*
Kirby SuperStar*
Kirby's Dreamland 3*
Legend of Zelda: A Link to the Past
Lemmings*
Lion King, The*
Mario Paint*
Monopoly
Ms. Pac Man*
Out of This World
Pac Man 2: The New Adventures*
Paperboy 2*
Pinocchio*
Pitfall: The Mayan Adventure*
Scooby-Doo Mystery*
SimCity*
Soccer Shootout*
StarFox
Super Adventure Island*
Super Battleship*
Super Mario All Stars + Super Mario World*
Super Mario Kart*
Super Mario World 2: Yoshi's Island*
Super Star Wars
Tetris Attack*
Timon and Pumbaa's Jungle Games*
Tiny Toon Adventures: Buster Busts Loose*
Tom and Jerry*
Top Gear*
Toy Story*

Those titles marked with a star (*) are those that I have had since I was a kid (and since before my local GameStop had stopped selling SNES games.) Does anyone know of any games that I would enjoy that I don't have here? I could perhaps put a request in through Game Universe and ask them to hold a copy if they get one in. I already have compiled a list of games I want below:
Chrono Trigger
Earthbound
Final Fantasy II
Final Fantasy III
Illusion of Gaia

although I can't think of any others :\

[Nirvana]

I simply want something with great replay value. I always look for that when I read reviews of games I think about buying.

[The 1 2 P]

I simply want something with great replay value.

Seconded. When I can play a game a second and third time and still be enjoying myself, that means I'm having tons of fun. During the last gen(and the current one) that usually equated to online play. With online play I will be enjoying the same games over a period of years instead of days.

Beyond that, great music is important too. I also like revelations as long as they are pertinent to the story. Just having a half baked surprise for the sake of saying "we have a surprise in our game" doesn't work for me. I like those things that you never see coming(Star Wars: Kotor's Revan revelation comes to mind).

Finally and perhaps most important, the game has to be fun. Why else would I still buy current gen versions of Tetris. It has that everlasting fun gameplay appeal.