Lots of problems - try the free one first – BoxyTunes - audio, music, and podcast player for Dropbox Review

Problems 1) Only "sees" about 2/3 of the songs. Not sure why but someone else mentioned that it can't play .mp4s 2) To get boxy tunes to see the song I have to start playing it on my PC from inside dropbox and then stop it, go to the next song, repeat. After that they will show up in my music folder. 3) After that, there's no "add all" option in boxy tunes. To add a song to the playlist (and there is only one playlist) you navigate to it and tap it, I then wait 11-12 seconds for the file to download (3mbps wifi connection). Then you repeat that, one by one, for however many dozens or hundreds of songs you have. 4) There's no delete from drop box option. You are stuck still managing your music from your computer not your device. 5) You can delete songs from the playlist but re-adding them requires the same 11-12 second each song process. If you still want to try it, there is a free iPhone version.
Review by Jeremythebullfrog on BoxyTunes - audio, music, and podcast player for Dropbox.