I can’t see it as embarrassed or insane. A shit-eating grin, as described above, is smug beyond anything else. I’ve always sort of thought of it as a grin so self-satisfied that when you see it, all you can think is, “Eat shit, fucker!”
Lots of interesting answers.
It would be interesting to find out what year the term was coined and the context for it.
I’m guessing it’s a southern good ol’ boy term, they have a lot of great ones. 
Since it is obvious that nobody took my first reply seriously, I feel I must explain why my answer completely explains the meaning of a “shit eating grin.”
First it is necessary to define a “shit eating grin”. It is as follows:
At a church party, Ms. Lulu gets glassy eyed and starts giggling. Someone askes “Okay, who spiked Ms. Lulu’s punch?” Everyone looks around and someone says “Look at that shit eating grin on Sam’s face”. Even though that isnt a nice thing to say in church everyone recognizes after seeing the smile on Sam’s face that he is the guilty person. Sam should have tried to surpress the grin, but he couldn’t help it. He’s caught and can’t deny it.
Now picture an opossum. It has the appearance of having the exact kind of smile on its face. It is an animal that we all consider repulsive, since it is not only ugly but it is a scavenger. It eats things that we wouldn’t eat. There really isn’t anything that an opossum can do that it shouldn’t do, except eat shit. Even an opossum shouldn’t do that.
Now picture that you’re driving down the road and in your head-lights you see an opossum and he is eating shit. He will still have that look on his face, because he couldn’t help it.
So Sam couldn’t help having that look on his face and the opossum can’t help having that look on his face. That is why that look is called a Shit Eating Grin.
That was what I said…
Busted, no denying, no good reason.
No helpful thoughts, just letting you know that OED has it first from 1957.
Another one of those occasions where I realize I’ve just assumed I was right and never thought there might be an alternative explanation.
See, I’ve always figured it was based around babies.
Ever seen a baby that’s done the delve-into-the-nappy trick and painted the wall, the crib… and smeared it around their mouths? I’d always assumed a ‘shit-eating grin’ referred to the baby’s wide-mouthed expression of pure glee.
Frankly, I’m kind of relieved to hear a less disgusting interpretation.
Babies are gross, m’kay?
Since it’s a guessing game, I thought it meant you were so happy you could eat shit and still grin. You are smiling, it is either inappropriate or not obviously called for. If you won the lottery and nobody knew, and then you had to eat shit, you would still smile. Nobody can do anything to ruin your happiness, even if they made you eat shit.
There is only one time when someone would smile and eat shit, and that’s if they had some great news inside that made it all okay. So when you see someone smiling despite the fact that you wouldn’t expect them to be, you know they must have some secret reason for grinning, and you think, “she doesn’t care, she could be eating shit right now and she’d still be smiling.” That’s a shit-eating smile.
I don’t think it is the smile of someone who secretly ate shit and enjoyed it. It is the other way around. Eating shit would not spoil their happiness.