App World does
have a music app that lets you download music - BBM Music. It's connected to your BBM. It's a subscription service but I just read they are giving 4 or 6 months free for new accounts depending on your country - if you are in a location where it's supported.
Here is the information about the extended free trials. New BBM Music Offer Means Free Music for You «Inside BlackBerry - The Official BlackBerry Blog
More info about BBM Music: BlackBerry - BBM Music - Download BBM Music - BBM Music US - Messenger
I'm subscribed to it and I think it's great - well worth the $4.99 a month. You can have up to 500 contacts and if they each have 50 songs, you have access to 25,000 songs You can add new contacts from within the app so they don't all ahve to be in your BBM contacts. Right now I have just under 10,000 songs I can listen to. You can also purchase songs though the app.