Everyone talks about Street Fighter or Tekken, but let's hear it for the weirder, unique, underrated, or forgotten fighting games out there.
My favorite is a Gundam game. Federation Vs. Zeon and it's sequel, Gundam vs Zeta Gundam, made by Capcom. The original games in the Gundam Versus franchise of games. imo the series was at it's best when it was handled by Capcom.
Time Killers was hilarious. You had separate buttons for each of your character's limbs and your head. You could sever your opponent's individual limbs, rendering them unable to perform certain attacks, and decapitation was an instant KO. The lead designer described it as having been inspired by the Black Knight scene in Monty Python and the Holy Grail.