Fun to do these...I haven't made one in a long time so i'll take a crack at it. I'll stick to a top 10 and won't cheat, and won't include packaged games (Mario Allstars for example).
Hard to remember since I don't play older video games much, but I remember most of my favorites.
1. Final Fantasy VII - A magical, amazing game.
2. Super Mario World 2: Yoshi's Island - Fun, fun game. Fantastic gameplay. The original is also a personal favorite, but the sequel was much better.
3. Super Mario Kart - Classic
4. Quake (Original) - Multiplayer greatness. I've probably spent more than 1500 hours
playing online, and less than 3 hours playing single player.
5. The Legend of Zelda: A Link to the past - Classic
6. Mega Man Legends - This one just struck a chord with my I guess, I thought it was excellent and no one else seemed to notice it. The sequel was pretty bad sadly.
7. Deus Ex - Very fun/interesting game, way ahead of it's time. The "sequel" was horrible.
8. Paper Mario 2: The Thousand Year Door - This one also struck a chord with me, probably in part because I'm a huge mario/nintendo fan and the did an excellent job with both paper mario games, really looking forward to the next one.
8. Katamari Damacy - Brilliant, funny, quirky, tons of fun. Pure gold. This applies to all Katamari games as of now.
9. Actraiser - Great 2d platformer, with beautiful music from Yuzo Koshiro (get Actraiser Symphonic Suite
link )
10. Pilotwings - Another SNES classic. The N64 sequel wasn't too good, I think there's one in the works for Wii as of now.
That's all that comes to mind for now. Some honorable mentions... I thought the original Metal Gear Solid was perfection, just much too short. Street Fighter II was awesome, just not a whole lot of depth. Skies of Arcadia was a great RPG for the dreamcast, I'm just not a big RPG fan. Speaking of RPGs, gotta mention one of my favorites Super Mario RPG, it was superb, lots of fun. Zelda Ocarnia of Time is a classic for sure, I just haven't played through it, just played in bits and pieces. I remember enjoying the Donkey Kong Country games a lot. Tetris attack i consider to be the best puzzle game of all time. Shadow of the Colossus was amazing, they just made it too early and it looked bad and could barely run on the PS2, I wish they waited and released it on the 360 or something instead, it's still a beautiful game, but the PS2 struggles with it. I would of listed Diablo II above but it stole too much of my life away...not that I have a life. And gotta give a shoutout to Bubble Bobble.
I'm done babbling for now.