When it starts getting played in contexts that are a totally inappropriate match for the circumstances. Classic examples include when "Who Let The Dogs Out?" started getting played at every sporting event (because what we all want to hear when watching sports is a song about inappropriate party farting) and the entire Black Eyed Peas catalog at any event ever (except, perhaps, a bonfire of BEP CDs). The other circumstance, for completeness's sake, in which you can tell your song is overplayed is "Hey Ya!", which was simply played far too much. (These songs become good after a rest--"Hey Ya!" is just as excellent now as when it began; "Who Let The Dogs Out?" is bad.) Our latest example:
We were recently played this song throughout the NBA Draft, and for an event ostensibly about the happiness of new beginnings and the future, it's odd to play a song about a bitter breakup containing the line "WE COULD'VE HAD IT AWWWLLLLLLLLLLL!" This sounds like the sort of thing you hear after the disastrous post-career bankruptcy, not the promising beginning.
In other words, totally inappropriate. The question is will "Rolling in the Deep" become "Who Let The Dogs Out?" or "Hey Ya!" While "Rolling in the Deep" is not as good as "Hey Ya!", I expect it to be more like that song--it is, in fact, a pretty solid song. But overplayed.