I find that more often than not the best songs are not played on the radio... although I am guilty of this often, as a practice, I try not to typecast popular rock bands.
My parents never cared for Elvis' music because it was overplayed. My older brother loved Elvis from a young age so I got to hear quite a bit of it growing up.
Elvis, The Beatles and The Stones were played way too much and did get on my nerves, but looking back each band has a few tunes that are really quite good if not brilliant. Some of them were even played on the radio.