And only 4 buttons...
Samurai Shodown 1-3 are among my favorite fighting games. I personally do not like 4 because it changed up the mechanics too much. I never really played much of the series beyond that so I can't really speak to any of the games after that.
I also like the
World Heroes series even though it feels like it has long been forgotten by history. (This is from playing the SNES ports of 1 and 2.)
Now I know Fighter's History has its issues but I still think the sequel on Neo Geo,
Fighter's History Dynamite, is a solid game and a fun time.
I've never played it but I've heard that
Breakers is a good fighter (but it also copied quite a bit from Street Fighter). I have also heard that
Waku Waku 7 is a good game but also kind of crazy and wacky.
King of the Monsters is a fun little Kaiju-based free-for-all brawler/wrestling game (but I think the fun factor is somewhat dependent on the number of people playing). I don't remember much about the sequel because I can't remember if I have ever played it.
3 Count Bout is a fighting game that is disguised as a wrestling game which I think is kind of similar to Saturday Night Slam Masters.
Bust-a-Move / Puzzle Bobble is a fun and challenging "tile"-matching action puzzle game that I always enjoyed (even though I wasn't that great at it).
Spinmaster is a fun and cartoony action platformer by Data East which has 2 player co-op.
Windjammers is a sort of Mario Sports-like take on 1-on-1 frisbee tennis with a lot of flash and style but I don't think the gameplay is very deep.
Zed Blade / Operation Ragnarok is a shoot 'em up that doesn't break much ground but I always liked the style and feel of it. And I think the same goes for
Sengoku but it's a beat 'em up.
Crossed Swords is an action game based around fighting monsters as a sword and shield using knight that uses a first/3rd person combat perspective sort of like the arcade version of Punch Out. (Also has co-op.)
And finally I will mention a Neo Geo game that I have never played but was always incredibly intrigued by -
Magician Lord. It is an action-platformer where you play as the titular character. The gimmick / draw of the game is that you can use power-ups to transform into different characters with different abilities.
Ninja Combat (it's no Final Fight, not even close, but you can strike from a distance with shuriken and it's got some ninja acrobatics that are fun. Also, hee-larious voice samples!)
I don't remember the voice samples but I do remember it being a solidly fun beat em up (but also a quarter-muncher like all its kind). It also allowed you to play as the boss characters after you defeated them.