Sorry if this sounds like an ad for Sony, but I have been very happy with my Sony mp3 cd player. It plays mp3 disks that I burn with WinXP or Nero just fine. I haven't even bothered to install the Sony software onto my computer.

It's also easily as thin as any regular cd player. The best feature is the battery -> great lifetime + rechargeable. The player only spins the disk for about 30seconds as it reads the song data. Then it stops and waits for the next song.