Many of us stash their whole music collection on Dropbox and forget all about it for a while. The next time we want to listen to some old tune, we (at least I) feel too lazy to sync the directory or search and download the file. Here are some ways to listen to your music on Dropbox without literally downloading them.
Clementine is an awesome music player that can stream music not only from Dropbox but from other services like Box, Google Drive and OneDrive. Just search and play!
Web service to stream music from Dropbox. You can browse all your directories and listen to your favourite music.
Web service that authorizes with Dropbox and needs you to create a directory inside Dropbox folder tree. You can move the files you want to listen to under that directory and streamboxr will play it for you.