I listen to bbc radio through moodio. Set up an account & add stations on your pc and then listen on your BB.
Just be careful as there is a normal site (to set up your account) and a mobile site for your BB.
Good luck and contact me if you have any problems.
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I personally use slacker radio. I have used it online for awhile and was excited to see that I could load it on my BB as well. You can pick a favorite artist and it will create a station with like artists for you. You can ban songs, or have them play more often as well. I'm a big fan.
i like slacker's interface and the options you have with it, the quality is a lot higher too. buttt... i chose pandora cause it just a whole lot faster and i dont mind the quality of music