Android - How do I play MP3s from my Dropbox?

Download the app called Rescan Media from the market, run it then go back to your Music player. The music that you downloaded from dropbox should now show up. There are other ways to force this media sync (unmount / remount SD should do it) but this app makes it just the press of a button.

In Dropbox, simply add MP3s to favorites and they become available in a stock Google Play Music application (Tested in Android ICS)

If you export the tunes to the SD card rather than the music app then they will show straight up in the music player. Just a little annoying that you've got to do them one at a time rather than as a group.

Dropbox > More > Export > Save to SD card > select Music folder