1. Mario Kart (SNES)
2. Battlefield 1942 (PC)
3. GoldenEye 007 (N64, tie)
3. Frontpage Sports Football Pro (PC, tie)
3. Battlezone (PC, tie)
Hard list. Bad me, ties at the end
But I decided to define them by "favorite at the time" on a rolling scale based on time played * enjoyment. Those games have all been exceeded in terms of quality, but for their time they absolutely rocked (even though each was terminally flawed by today's standards). Special mention to Conker's Bad Fur Day, WCW & WWF Asmik games, SMB3, Madden & NCAA, Gran Tourisimo, Mario Party, Worms, MoO, Reach for the Stars, Spaceward Ho!, Street Fighter 2, and Starflight. Interestingly the above list may not be the "best" games I have ever played (Mario 64 and Zelda Ocarina of Time are easily at the top of that list).
Great games, just not my top favorites. Loved them, a lot of fun, just not my style (note the running theme of MP games, even way back on the 286 and SNES). My modern list of "my best" favorite games would be something disgruntled, like:
1. Half-Life 2 & Counterstrike (polish, innovation, evolution, quality, and longevity--everything good about modern games IMO and barely missed my top list above)
2. Madden (evolving slowly, and a ton of issues left bare... but only/best football game on market and years of development show with solid base of polish, if not lacklust development of late cannot undo the years of incrimental evolution and features)
3. Battlefield 2 (great concept, quality core, bugs, lack of support and timely followthrough, poor dev-community relations, movement toward managed servers, and some unbalanced issues plus originally horrific online filter for a MP game, plus late coop support, leave a bad taste in what is really a great game--and could have been even better with more focus/attention)
3. Mario Kart Double Dash!! (Great core, a tad too slow and some issues--no online support, no 4 player GP in single karts, limited to 8 karts, no hop, and the continued digression away from pure racing skill, needs another Cup and some more unique tracks and custom Cup where you choose the tracks--but overall a polished game with fun coop and by far the best looking and playing kart game on modern consoles)
All but the first are examples of good games, but bear signs of some of the more annoying "features" and developments of modern gaming. Hence they were unable to crack my top 3 (err 5).