I remember a number of songs that sounded very catchy to me at first. I listened to them like two dozen times and then I got completely sick of them and wondered why I ever liked them in the first place. For example, I think about everyone had this with Fireflies by Owl City.
On the other hand, there are some songs that I've listened to hundreds of times (according to iTunes) and I still love listening to them. In moderation though, I just can't keep on listening to the same songs forever.
Anyway, I guess it all depends entirely on the song.