Super Mario World (SNES) - First game I ever owned. Still a favorite to this day. I'm always surprised when I re-play it that I still remember all the secret areas. One of the best games ever!
Super Mario Kart (SNES) - The original kart racer. Lots of great memories playing this with my sister, and my childhood best friend.
Halo:CE (Xbox) - One of the best FPS campaigns ever. I've played through it several times on legendary solo. Though I'm more of a campaign guy, playing Halo:CE on LAN is one of my favorite gaming things to do.
Need For Speed: Hot Pursuit 2 (PS2) - Easily my favorite arcade racer. Great roster of exotic cars, fun arcade handling, and awesome tracks. Took me a while to finish all the races.
Borderlands (Xbox 360) - This is one of the few games this generation that has managed to hold my attention long term. I got it in its release month and I still enjoy playing it. It's fun to shoot, the loot mechanic is addictive, and has excellent DLC that really adds to the game.
Oblivion (Xbox 360 & PC) - I've spent many, many hours playing both this game and its predecessor Morrowind. I have yet to "finish" either one (partly due to game breaking bugs and lost save files). But this game isn't really about finish the storyline for me. It's about exploring, finding side quest, shaping my character, and doing whatever I choose to do.
Honorable Mention:
Gran Turismo 1,2&3 (PS1&PS2) - I used to love cars, and I played the crap out of these games (100% completion on 1&2, 75% on 3). Once I got to the endurance races in GT3 I called it quits, and didn't play another racing sim until Forza 3, which I also quit after getting to the endurance races. Why can't you just save midrace?!
I tried my best to keep my list relatively short, which was a challenge. I've owned a SNES, Gameboy (original and color), PS1, PS2, Xbox, Xbox 360, PSP, PS3 (my brother also a Wii), and now have a desktop gaming rig as well now. I tried to keep it to games that held my attention for long periods of time, and games that I find have a lot replayability. Sorry if I spent too much time talking about the games