Firstly I'd like to say that "Aqua Teen" is one of the funniest animated shows, mixing absurd situations with absurd characters who do absurd things. But great comedies (which this is) are more than simply absurd, they're smart. They bring us into the world of the cartoon and have us relate to each character. So I'm going to look into why this is a "great" animated comedy, merely because of its characterization.
Carl is a poor, single, overweight man on welfare whose main cares in life consist of the cardboard cutout of a girl advertising beer, his car, lawn, swimming pool, and reminiscing of the old days, when he would get hammered and go to rock concerts. The interesting part about Carl is that he never admits to any kind of friendship with the Hunger Force, yet they are in his swimming pool almost every episode, and all of them, through all the bickering, get along. Even though Carl is always apparently miserable, his true joy comes from the friends he presently has, which he never addresses. How many people do you know who want to go back to the "good ol' days" when everything was simpler and sweeter, but fail to see the good things in their present life until they're reminiscing about it twenty years down the line?
Shake is funny. Very funny. Perhaps the funniest character in any cartoon show ever. This is achieved in an ingenious paradox. While he is cruel (esp. to Meatwad), self-indulgent, and egotistical with absolutely no sign of empathy, he is the most likable character in the show. Why? I think it's because of his simplicity, like a more intelligent form of a child (aren't children selfish and always unsatisfied?), and who can blame a child? All you can do is laugh at their behavior.
Meatwad is also like a child, but instead of being the kind that doesn't share (like Shake), he is the kid that gives his toy truck to the new kid in school to play with in the sandbox. While Shake is the most likable, Meatwad is the most lovable, and is even more-so because he is missing a brain (does Shake's intelligence give way to vice? If one looks at the episode where Meatwad becomes smarter than the other two, it would seem so). But we can never "like" Meatwad, because we can't associate with him in his stupidity, we can only love him like a small, cuddly dog. Meatwad's voice sounds like a mixture of Yoda and Terrence from SouthPark, which is, somehow, indescribably perfect.
Frylock's character acts many times as the mediator in arguments. He is highly intelligent, humane, but at the same time conceded in his intelligence and humanity (when Meatwad gets a brain and surpasses Frylock's intellect, Frylock becomes jealous and angry). He is individually the least funny of them all, but this is on purpose. He is the sanity in the absurdity, accentuating that absurdity.
Perhaps the best aspect of the cartoon is its lack of development. Nobody changes (at least in character) from one episode to the next. Carl is still poor and resentful, Meatwad is still lovably stupid, Shake still conniving and hilarious, and Frylock still intellectual and, well, normal.
It is impossible to keep a straight face during any episode of Aqua Teen Hunger Force (most especially when the Mooninites make an appearance). But if one allows himself to watch with an active mind, you will see a satire on human nature, which inclines the characters to do some absurd things. But are we really ones to laugh at these characters in their absurdity? Wouldn't we be actually laughing at ourselves? Of course! That's another part of the genius. It takes human faults and shows how stupid and fruitless they are. And by laughing at ourselves, we are in fact reflecting upon ourselves.