Now, I know many people over at ATW like to post actually terrible covers as being their favorite, as a joke, but let's try to compile some really great ones. I'll go first:
This guy, Michael Skinner, does acoustic covers of tons of pop songs, and Weezer is his favorite band. He does a great one of Falling For You, among others, but I like this odd swing version of Don't Let Go that he does.
(For now, it's just a link until someone can tell me how to embed videos.)