I really like Mighty Final Fight for NES (or on on Capcom Mini Mix (GBA), which is the port I own these days).
As for the Arcade original, I was a poor kid and didn't get much cash to waste on arcades.
I think I remember renting the SNES Final Fight (on a friend's system) once and liking it well enough. I never ran across a good deal on Sega CD port (which is what I ended up owning in that era), so I never REALLY got into it back in the day.
Otherwise, an occasional playthough on Capcom Classics Collection is usually a fun time and you can't deny that the original arcade was pretty groundbreaking (or a good evolutionary step for beat-em-ups at the very least).