Yesterday my partner bought the app TuneIn for her iPad. After playing around with it, I can really recommend getting this app for your mobile device. Quite a few devices are supported: iPhone/iPad, Android, Palm, Blackberry, Samsung Bada.
We can listen to 30.000 radio stations from all over the world but the feature we really like is the ability to listen to BBC stations. There's even an option to click on a specific programme and get a list of previous episodes. Absolutely great for us because we live outside the UK and can't subscribe to podcasts that contain copyrighted material (like BBC Radio 3's Composer of the Week). It looks like the app supports iPlayer streams. Bitrates could be a bit higher for the BBC streams.
The app also has a timed recording feature. alarm and sleep functions and gives extensive programme listings.
Our iPad can stream directly to our Airport Express so playing through the stereo is incredibly easy.
If you like classical music I can really recommend Dutch Radio 4. Andrew Everard has recommend this station before. It streams at 256 kbps.
All I can say is WOW!
If you want to listen to the radio stations on your Mac or PC you can go to this website: www.radiotime.com. It offers the same features as the app but is free.