While the portable media players VLC & MPlayer are great, they're not so great for playing just music files, especially from playlists.
I tried both but their lack of playlist functionality is frustrating.
I also tried a portable app called soprano but it's lacking in playlist-usage as well.
I did find one great, lightweight candidate: yPlay - http://www.spacejock.com/yPlay.html
"yPlay is a freeware MP3, Ogg*, WMA, WAV, FLAC* and Midi player with multiple playlists and a light, clean interface."
I installed it directly to my USB drive, and it's working, but not fully-portably. (For instance, it plays music on my work pc, but was acting strange on my gf's laptop @ home.)
Please strongly consider this app for your list; I recommend it