For starters the
BBC internet radio has a huge selection of stuff, the vast majority of it being available on demand or you can listen live.
It's also very reliable, i've never had any problem with it but the bitrate does tend to go down from about 256kbps to around 45-ish. Doesn't really detract from anything though, the sound is still crystal clear.
The other thing I like a lot isn't internet radio but a music show called
'In the Attic'. It's hosted by Rachel Fuller (Pete Townshend's girlfriend) and a geezer called Mikey (the pikey) Cuthbert and is live music from the hosts, Pete Townshend & occasional guests. So far since In the Attic is following The Who around on their festivals tour they've had Razorlight, The Flaming Lips, E from Eels, The Kooks, Magic Numbers, Rosehill Drive, Shack, Foy Vance, Martha Wainwright and several others all doing live acoustic stuff. Best of all, it's free and it's looped again afterwards.
Jam it back in, in the dark.