I own DS, Wii, PS3, PS2, Game Cube...
I play a lot of popular RPGs like Final Fantasy (1, 3, 6, 7, 8, 9, 10, 12), but I like a lot of classics and play them over and over. Mario 1, 2, 3, Super Mario World... I'm replaying Paper Mario: Thousand Year Door for Game Cube for the 3rd time these days. Zelda is also a lot of fun. Mega Man (though I am horrible at it, I keep at it until I win).
I have a ton of Wii games but am not crazy about all of them. Raving Rabbids TV Party is highly recommended. Not only do you play as crazy rabbit-like creatures, you get to dance and do all kinds of crazy things. I also enjoy Wii Fit (hula hoop!). Wario Ware is fun as a party game.
One of my favorite games is Mario Kart: Double Dash (Game Cube). Best racing game in my opinion.
PC: Starcraft JUNKIE. I can't tell you how many hours I probably clocked in my life on this game. Still play it online every now and then, but am eagerly waiting for Starcraft II. Diablo II was another crazy one I spent way too many hours of college playing.
If you have a DS, I highly recommend: Phoenix Wright: Ace Attorney 1, 2 and 3. Hilarious game about a lawyer guy doing cases. Another dark horse: Hotel Dusk. It's a really good game but it was not marketed all that well but was sort of a sleeper hit. Also, Elite Beat Agents if you like DDR (all platforms) or Tap Tap (iPhone). It's crazy rhythm bopping fun! Another weird game with lots of puzzles to solve: Professor Layton and the Curious Village. It's just filled with mini puzzles and it's very well done in my opinion.
Of course, I love to play Kirby games! I missed Kirby games in my childhood but have been playing all the re-releases on the DS platform. That's where my bunny Kirby gets his name!