I just save myself the aggravation and don't listen to the radio unless there's a game on of some sort. However, for someone with a wide yet (apparently) very picky taste such as myself, Internet radio is great as there are stations specializing in most varieties of music you could imagine. Other than that, I just put on a CD or tape or mp3s or whatever.
But...just to keep things on topic...
If I were listening to the radio, I would change for the following songs/genres/artists:
Almost all R&B
Most rap
Pretty much all commercial dance
Pop-rock
nu-metal
Hoobastank - "The Reason"
Disco (although I suppose that fits in with commercial dance)
Just about all the Black Eyed Peas singles (Fergie is yum though
)
The Chemical Brothers
Fatboy Slim
Emo
Anything any Australian Idol has released that I've heard so far
Most country that I've heard (though I'm willing to give the genre a chance if someone will show me "the good stuff")
Creed
Anything Nirvana will generally cause me to inflict violence on some inanimate object in close proximity
Any song that commands me to dance is going to suffer violent insubordination
I think that just about covers it.