It's pretty ridiculous to try and pick a favorite game out of 25 years or so of playing them. So many games were great because of their innovations, but have been superseded by people polishing those innovations.
People love their N64 Goldeneye, but to me it was an utter joke as I had already been playing QuakeWorld online with a 3DFX card. When my friends later raved about Goldeneye I just couldn't care because the N64 controller, the drastically lower resolution, and the drastically lower framerate made it unplayable. I mean seriously, that game rendered at what, 320x240, of which I'd get a whopping 160x120 as my 'screen' ono a good old fashioned tube television? Utter absurdity.
Then again, if you weren't into PC gaming at the time, then I could see why the gameplay and various innovations might draw you in.
To me, the original Half-Life is one of the best games of all time, better than Half-Life 2. Of course Half-Life 2 is probably superior on every level, but it didn't have as much of an impact to me.
I guess the best I can do is throw out a vaguely chronological list of games that to me were near perfection in their historical context.
Time Pilot - Classic arcade favorite for me. I liked that you had to actually steer your ship and plan your course rather than be able to turn on a dime. That made the dogfighting so much more satisfying.
Mike Tyson's Punch Out - To me, it had possibly the best graphics on NES. The character artwork was just amazing. The gameplay was ridiculously satisfied as you learned your opponents' weaknesses and eventually learned to dominate them. Fantastic music as well. This is one game that I can play today and still have as much fun with it as I had back then.
Phantasy Star - For the 8 bit generation this game was a complete marvel. I thought it blew away the likes of the original Final Fantasy and Dragon Quest (Warrior?) games on basically every level.
Final Fantasy II and III (using the fucked up US names) - Square put out quite a few great SNES role playing games, but for my money I'd take these over Chrono Trigger any day. I'd argue that Chrono was just too damned easy. The middle of FF3, where you get the new world map utterly blew me away at the time. I thought I was about to win the game
A Link to the Past - The best of the Zelda games. It's basically the perfect 2D action rpg. I really don't see what the hell people liked so much about Ocarina of Time. I thought the 3D on N64 across the board was just clumsy. N64 for 3D is how I feel about Atari 2600 for 2D. It's just at such a primitive level that it's painful to try to play most of the games.
Super Mario Kart - For me its been eclipsed by Mario Kart Wii, but it was a fantastically addictive game. Aside from mastering the various Grand Prix races, I spent countless hours racing my time trial ghosts and playing battle mode with friends. You know you have a good game when it has multiple modes and you feel compelled to play them all to death.
Super Mario World - You need a mario game on any best games list... much like my Zelda choice, SMW wins because it had refined the formula to perfection, and it came at the 16-bit pinnacle before the shift to stone age 3d graphics. The persistent save file and the opportunity to '100%' the game seemed pretty new at the time as well. It really gave me a reason to play through every nook and cranny. Unlike say SMB1 and SMB3 where I was just trying to beat the game, and lo and behold there are warp zones to skip 2/3 of the game!
Doom/Doom 2 - Maybe Wolfenstein could've been here... but there was nothing quite like the first time I booted up the Doom shareware on my 486. The technology blew me away. This game also gave me my first taste of deathmatch. Utterly amazing, and it actually plays pretty well today. Most shooters have lost the ultra fast feel that Doom had.
Civilization 2? 3? maybe even 4? - Kind of hard to choose, I never played the original but each of the sequels seemingly managed to improve some things while screwing up others. I've lost entire weeks to single large map extravaganzas in all three versions, so what can I say?
Kings Quest VI and Space Quest V - KQ6 for the awesome multimedia version. SQ5 for the command of your own garbage scow in heavy Star Trek parody form. You could argue for some Lucastarts gem here. Day of the Tentacle or Monkey Island, but the Quest series felt more hardcore to me. You could actually die, and in fact the hilarious methods of getting yourself killed were part of the appeal.
Star Trek 25th Anniversary CD-ROM Edition - Great adventure game, it was awesome to have the voice acting as well. The episodic format was pretty cool and really made it feel like the show. I loved that there were multiple ways to solve the episodes as well and that you would be graded on your performance. Even the space combat was pretty fun in its own primitive way.
X-Wing - I'll take this over its sequel TIE Fighter any day. TIE Fighter was a bit disappointing since instead of pwning rebel scum all day they decided to throw you in a lame civil war plot. Don't make a game called TIE Fighter then cut short my stint as a bad guy. That's just cheating. Also, sorry, TIE Fighter just didn't have anything as epic as the final series of missions at the Death Star culminating in a speed boosted trench run. That was bad ass!
Alone in the Dark - The original on PC back in 1992 or so. Far more creepy and atmospheric than Resident Evil, which ripped it off right down to the creepy mansion. Of course Resident Evil replaced the Lovecraftian horror with cheap comic book mutant nonsense, and somehow stole all the glory for the the survival horror genre. But some of us know better.
Command and Conquer - Awesome single player, and the multiplayer really shined over Warcraft 2, despite the fact that the lower res graphics couldn't really compete with War2, the fact that the two factions were totally different and still decently balanced really set it apart. Unleashing a nuke in multiplayer was beyond epic. I have nothing but fond memories playing 2v2 matches over Kali.
Half-Life - Probably the first time an FPS had its storyline completely captivate me, right from the opening tram ride. The gameplay was tight as well. Just extremely polished from start to finish. I even liked the low grav alien sections which I guess a lot of people didn't dig.
Mercenaries - Probably my favorite open world game so far. The entire GTA3 series deserves an entry as well. But Mercenaries was just epic. The setting, the wide assortment of military hardware. The xbox version was the first time console games had competed with PC for me in a very long time. Shame about the sequel though
Warcraft 3 - My favorite RTS of all-time. At first I was dead set against the concept of heroes, but I soon learned to appreciate the extra levels of strategy they added to the game. Do you use one hero and level him up as fast as possible? Do you go all out with 3 and hope you can keep them all alive long enough to become useful? The battle.net matchmaking was pretty damned good as well.
Geometry Wars: Retro Evolved - The ultimate retro game. It's a mesmerizing symphony of explosions. The dual stick controls are perfect. Just you, a couple of lives and bombs, infinite enemies and a score counter. That's exactly what old school arcade gaming is about.
Call of Duty 4 - A CoD game definitely belongs on the short list. CoD4 wins out for the amazing single player and multiplayer package. The bullet penetration. The killstreak rewards, the tight gameplay refined from IW's first two efforts.
Rock Band 2 - The best of the plastic instrument games so far. It lets me play two entire Megadeth albums. It's definitely on the short list.
I know I've missed a ton of great games, but this post is already getting ridiculously long, so I'll leave it at that for now.