Getting the mainstream ones out of the way first: 3s, Garou MotW, ST/2X, Tekken 3 (PS1), UMK3, MvC2, CvS2, SC2, KOF '98, Vampire Savior

Got it? Good. But have you played:
Jackie Chan in Fists of Fire: Strange Mortal Kombat-looking game with three Jackie Chans, but surprisingly accessible
Fighter's History Dynamite/Karnov's Revenge: Karnovember is coming! A 1994 fighting game that held up very well
King of Fighters '95: A prime example of SNK's old school style
Fighter's Destiny and Toy Fighter: 3D fighters where certain knockdowns earn you points, and first to 5 or 7 points wins
Street Fighter EX2 Plus: Arika's quirky take on Street Fighter with plenty of unique characters and mechanics
Slap Happy Rhythm Busters: Fast polygonal 2D fighter with simple controls and supers that make a rhythm action game happen
Teenage Mutant Ninja Turtles Tournament Fighters SNES: The good Turtles fighting game. Fun mechanics to learn and break.

Edit: Added videos for the games that didn't have links to a wiki