I think a lot of this discussion is just an unwillingness to differentiate between "gimmick" and "personality".
A gimmick is someone like the Undertaker, Boogeyman, Deuce & Domino, Umaga, etc. These people are playing characters that aren't just reflections of themselves. Umaga isn't really a savage beast...Undertaker isn't really able to summon lightning and resurrect himself and so forth (obviously, haha)
Some wrestlers don't have a gimmick, but they just have a personality. For instance, Batista. He isn't coming out dressed as an animal or anything, he's just a big, tough guy with an anger management problem. Shelton Benjamin and Elijah Burke just have the personalities of cocky and arrogant athletes. Kennedy has the personality of someone who is an asshole to everyone, but you love to hate him. Edge has the personality of the intelligent heel...a guy who runs away instead of being beaten to a bloody pulp, but actually steps up to the plate when he needs to, and will outsmart you into losing in the end.
So Cena used to have a gimmick when he was a rapper and such, but not now. Now, he just has the personality of a hard-working, morally sound, boy scout type of character. Cena isn't walking out to the ring with Scottish bagpipes playing, dressed in a kilt...he isn't wearing a mask and pretending to be a luchadore....he just has a personality, instead.