I complained earlier about musicians who arbitrarily change the timing and stress of songs to try to show emotion. Strong emotion will change the stress, and I don't really object to it. I meant the illogical changes: the pauses that make no sense; the crescendos inserted just to be different. Your rendition of a song will always be different from everybody else's, albeit in subtle ways. (or not so subtle--I don't always hit the correct notes) If you feel you have to make your version dramatically different from everyone else's, I submit that you don't have enough faith in your own music.
I think one reason we don't have enough faith in our own work has to do with what we think about the nature of creativity and genius. Someone (sorry, I've never had a good memory for names) expounded on the types of genius, claiming there was Beethoven genius and Bach genius. Beethoven broke new ground with new styles. Bach took old styles and took them to new heights. Both were truly creative, and both produced works of genius.
We all want to Beethoven-style geniuses, though; all pioneers, creating new genres. It seems more dramatic, even more noble, "to boldly go where no man has gone before." But it is hardly an indignity to become a master of some art, able to convey what you see in an idiom everyone understands. (In some of the arts, such as sculpture and painting, workers seem allergic to even trying to master old genres: everything has to be new and groundbreaking and therefore utterly obscure.
Because we want to be breaking new ground, we're often afraid to do something the way people have done it before; afraid of being "the same old thing." But a kiss is "the same old thing" too...