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.
When I was younger I really enjoyed the pacing of Killer Instinct: Gold (N64) and the technically superior arcade version Killer Instinct 2. It's not the best fighting game by any stretch and has its share of problems. It won't hold up compared to others from that era, like Alpha 3 or 3rd Strike, but it's fun all the same to execute the combos and I was very interested in the art style and environments. Also I think Glacius is really cool.