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.
Does Nidhogg count? Both of them. I love those games so much and it feels like other than around the launch of the first Nidhogg, I don't hear people talking about Nidhogg enough. It was my friend group's drunk party game for a while.
It's a lot "simpler" than most fighting games, but it's all about the push and pull with your opponent, predicting what they will do and reacting or striking before they can react. I don't know, I love it. It's probably cheap and definitely worth picking up if you want something to play with someone locally. Both games are good, but I prefer the raw simplicity of the original. The sequel might be more fun in parties, because it adds variety to the weapons.