I can't narrow it down at all so I'll just put some of the ones that have given me the most fun.
Multi player games:
Street fighter series, arcade cabs (especially, II TURBO, Third Strike, and Alpha 2)
Marvel vs. Capcom
TIMESPLITTERS!!!
Mortal Kombat II (arcade) and Trilogy (Sega Genesis)
King of Fighters series (2D)
BUSHIDO BLADE!
Boom Bots
Battletanx
STARSIEGE!!!!!!
Extreme G
Out Run
Initial D
ARC!!!!
STAR FOX 64!
Burnout series
Power Stone
BOMBERMAN!
Counter Strike (all versions)
Team Fortres (All versions)
DIABLO!
Command and Conquer (select versions)
Warcraft
STARCRAFT!
HOMEWORLD!
DAWN OF WAR!
QUAKE!!! (All versions)
Unreal Tournament
Magic: The Gathering (through Urza's Saga, that's when I stopped playing. Still got some great Alpha cards too)
RAINBOW SIX! (especially Rouge Spear)
JANE'S flight sims! (Especially F-18, and IAF)
FALCON 4.0 (Amazing multiplayer battles)
North & South (My very first tactics videogame)
VIRTUAL ON!! (Arcade and Saturn)
This list is getting wayyyyyyyy too long so I'll stop there but rest assured there are so many more that have given my friends and I years of stories and happy times. The single player games are an even bigger list so I'll hold off on those for now.
Edited so I could pop in D&D (rolling twenties since 1992), Warhammer, Warhammer 40K, Battletech, and recently, War Machines.