In chronological order of which ones blew me away first...
Marathon 2: Durandal - I've never played a game with action, storyline, and great graphics before and this one gave me all three at once. The second best game ever.
Harry the Handsome Executive - Very addicting, this is the one that got me into arcadey games.
Warcraft II - The music and graphics really set the atmosphere for this one, and it was the first strategy game I enjoyed.
Diablo - Same as above but stronger atmosphere and the first RPG I've ever enjoyed.
Lands of Lore: Guardians of Destiny - The game with the best atmosphere, ever. The Dracoid Ruins level is possibly the most captivating level ever made. The third best game ever.
Crusader: No Remorse - Graphically this game was and still is a beauty. The crisp coloring of blood, fire, and acid were very memorable and the action was top-notch. No game does violence better than this one.
Super Mario Brothers 3 (SNES version) - The ultra-happy music and bright colors hooked me into the platformer genre.
Starcraft - I spent almost 5000 hours playing this game on the BNet. The vast amounts of custom maps like Snowbound, Scary Movie 3, and Lurker Defence turned me into an addict.
Deus Ex - Hands down the best game ever. Everything I've said about games previous to this is present in Deus Ex and much more. Warren Spector made a classic and one I still play several times a year. This game owns my life.
Kirby's Super Star - Although short, the vast array of power ups and baddies gives this platformer great replayability, and it's the only one that really seems epic in my eyes.
Hitman 2: Silent Assassin - Finally, a stealth game that wasn't too linear. This game is not only great for sneaking around but when it comes to blowing out the brains of large groups of civilians, this one ranks high.
Mafia - The most polished game ever when it comes to artistry. Everything from the textures to the story and soundtrack are easily movie quality if not moreso. Playing the campaign is classic and the option to just roam around the cities while running over people is a great time killer as well.
Far Cry - A typical FPS on the outside, but when it comes to AI this game hasn't yet been beaten. They almost always attack in different ways during different playthroughs and aren't easily tricked like the enemies of most games before it.
Baldur's Gate II - No game I've played so far has as many quests to finish, as many items to collect, or as many areas to explore as this one. This game defines epicness.
As you can see, the 199x games outnumber the 200x by quite a bit on my list.