I don't know the band, but someone covered a cure song and they played it over and over on the radio. It sucked! If your going to cover something, at least put your own twist to it and make it worth listening to. It wasn't even as good as the original, so it would just p*ss me off every time it came on the radio.
Oh, just got the name off the web.. 311 covering Love Song (Cure)
For an example of a new twist on an old song, listen to Cake's cover of I will Survive (Gloria Gaynor). I like that one.
Edit: Oh yeah, I am not sure if this was the joke song of all times on the radio, but some band did a cover of the Annie song, the sun will come out. It hurt my ears.. Really it did.