I have the radio on almost continuously. (I watch very little television).
The alarm is set to switch on to Radio 2 (although I'll have probably been dipping in and out of BBC World Service throughout much of the night) and Radio 2 is my 'default' station in the car. If I'm actually up during the early hours I can listen to my favourite DJ (by a mile), the Dark Lord himself!
I also listen to quite a lot of the output of Radio 4 Extra and Radio 4 itself, as well as loads of stuff from ROK British Comedy:
http://rokradio.com/britishcomedy.php
Of course, when there's international cricket on, I'll be tuned to Radio 5 Live.
Somehow I still find time to squeeze in a bit of Radio 3 (mainly for the jazz and world music), with occasional excursions into BBC 6 Music and the BBC Asian Service.