You MUST've played on a Neo Geo. Loads of great arcade games ran on the hardware, and the beauty of the (very expensive) home console was that it was exactly the same hardware - so you had the ACTUAL arcade machine (minus the cabinet) in you own home in front of the telly.
The games that came on cart were heart stoppingly expensive, and the CD technology of the time was slow and expensive.
Fatal Fury, Sonic Wings (aka Aero Fighters), Samurai Showdown, the original Puzzle Bobble, and games that were prefixed Neo- (Neo-Bomberman, Neo-Mr Do) were all released on Neo Geo. I think Golden Axe and Double Dragon were ported to it as well. Mame runs 147 at the moment with more games available, but deactivated because the games are still taking money "in the wild".