I've always figured that Grimace is supposed to be a McNugget. Which, for all intents and purposes, is exactly what prole said up there. It doesn't take a huge stretch of the imagination to imagine McDonald's bleaching their purple goo and cutting it into horrible caricatures of severed chicken parts.

Anyway, look at few of other denizens of McDonaldland:

Fry guys are, I assume from the name, some demented ad agency's idea of what sentient french fries would be like.

Mayor McCheese is a similarly mutated cheeseburger.

Hell, even good old Ronald McDonald is just a frightening shadow of real clowns.

There's more, though. McDonalds has, in creating Grimace, given us a glimpse at their alter ego. "He" is a shadow of preprocessed bird meat, but also the shadow of McDonald's corporate mind. Grimace, they admit, used to be evil, but somehow became a not-so-evil fellow. It should be obvious that McDonald's does not want to be good. They want to be evil and feed innocent children their hideous lab experiments. They have created Grimace as a way to deal with the more-or-less basic human aversion to hurting kids; whenever Ronald makes Grimace look dumb, it is to reassure McDonald's that yes, they can force instincts away and continue to torture people. (Also note that intelligence is not an instinctual quality; therefore, Grimace being portrayed as stupid is another way of psychologically linking him to these instincts.)

You guys can call Amnesty International; I'm going to be sending McDonald's a copy of Wandlungen und Symbole der Libido and a list of good psychologists.

If only I spent as much time tonight's homework as I did on this....

Panamaus informs me that Grimace predates McNuggets. All this means is that we now have the answer to the eternal question of, "What part of the chicken are those nuggets supposed to look like?" The answer is, I now see, that they aren't. Chicken McNuggets are supposed to look like Grimace!!!
While this does invalidate a portion of my writeup, I still stand behind the Jungian bit of my theory.