This is all fairly subjective and is related to what games I happened to play first. All of these are computer games, as I never got much into consoles.
FPS: Deus Ex (2000). When I first got this I played it for 14 hours straight; it was that engrossing. Extremely long (which I consider a good thing), very detailed story, open ended mission design and immersive atmosphere. There were a few weapon balance issues though. This is a tough category with a huge selection of choices and Descent 2 and Unreal come close, but the incredible variety of goofiness that can be performed in Deus Ex puts it on top. I have spent more time screwing around with game glitches than playing normally, and I've fully played through the game eight times with all the side quests.
Space sim: Freespace 2 (1999). Duh. Very few choices here in the first place, but this had an outstanding storyline, great gameplay, versatile mod support and an overall polished feel. Independence War 2 was better in some ways but its clunky interface made it less enjoyable than it might have been.
RTS: Command and Conquer (1995). One of the first RTS games, and much better story and campaigns than any of the subsequent C&C games. Side balance was generally pretty good as well. I spent a lot more with RA than this because of its skirmish mode and mod capabilities, but this was easily the better game overall. TA was an excellent multiplayer game but had boring singleplayer campaigns and I never found Starcraft all that great. I haven't kept track of RTS games in the last couple of years though.
Multiplayer: Unreal Tournament (1999). I thought I would make a separate category here, since multiplayer games are judged quite differently from singleplayer ones. Lots of gameplay options, almost perfect weapon balance, excellent map design and great netcode for its time. I was a hardcore player of this for over two years and had risen quite high in the official ladders at one point. The newer UT games are better in many ways but Epic messed up the weapon balance from the original one. After six years, it also still has the best, most detailed textures of any game in existence.
Racing: Ballistics (2001). By far the fastest racing game out there. Very high fun factor, although it has some bugs and hardware compatibility issues. I still play this every now and then.
Adventure: Mission Critical (1995). The best plot of any game I have ever seen, and plots are what make adventure games. Puzzles were for the most part a bit too easy though. Holmes 2: Case of the Rose Tattoo had almost as good a story and was very long, but had some annoying bugs and I'm a little partial to sci-fi games.
Puzzle: Lemmings (1992). I played the Mac version of this, which had much better graphics and music than the original DOS one. Very original concept and a great game across the board. I was completely obsessed with this one for years and I still have the hundreds of custom level plans I had drawn on paper when I was in elementary school. Never did find a level editor for it though. The expansion pack, Oh No More Lemmings, was also great. The sequels had various issues ranging from being too easy (L2) to having a bad interface (L3D).
Fighting: Time Commando (1995). Not really a conventional console style fighting game, but it probably fits best into this category. The shortest retail game I have ever played, but there are very few that match this one for sheer fun factor. Had to include it in here somewhere.
Freeware: Infotron (1993). Old Mac game, a clone of the DOS game Supaplex but with better graphics and sound. I can't count how many hours I spent with this back then. Very polished game for a free one, looked more professionally designed than most retail games at the time. I drew many custom levels for this one as well, although I didn't find a level editor until very recently and only for Supaplex. Another tough category, as I had all sorts of great stuff on my old Mac (still fire those old classics up from time to time) and the more modern Lasertank comes close too, but this was probably the best one.
I haven't really played much in the RPG, TBS of flight sim categories, so I won't say anything there.