Well Soundjam MP for starters. It's what Apple bought and morphed into the iTunes we know and love today. I'm sure there were other programs that the more veteran mac users here will be able to fill you in on .
There were lots of Mac MP3 players before iTunes. There were AudioCatalyst, Audion, QuickTime Player, Soundjam (which became iTunes), MacAMP/MACAST, Winamp (briefly), more.
There was one, I can't remember the name, that I used to use because it used less CPU than the others. It was a drag and drop deal with just a plain white window and simple menus -- probably came from Info-Mac. [edit: Oh yeah, it was called SoundApp! ]
Yeah, I used MacAMP for the longest time before and after iTunes, in both its Classic flavor and OS X flavor. It was consistent with WinAmp (and I prefer consistency whenever I can get it) and it ran a lot better in OS X than iTunes did on 10.1 and 10.2.
iMeowbot covered the good and memorable ones. There's also an MP3 player for 68k, but I don't believe it predated iTunes, called MpegDec. It's useful if you still have a 68k-based Mac lying around.