Is it possible to get sick of REALLY GREAT songs that have just been played too much? I don't mean the amount you play them yourself cause that's controllable, but I mean songs you get exposed to a lot over a lifetime.
I've never grown tired of Maggie May. I could see myself getting tired of Roxanne since it's, like, THE Police song that everyone loves, after Every Breath (which are The Police's top 2 downloads on iTunes. Maggie May is Rod Stewart's #1.)
And though there was only one Beatles album in our household growing up (Sgt Pepper, which is still the only Beatles I own), I was still tired of all their Top Hitz by the time I hit my teens.