Pet the Dog: The one time Shake did something nice for someone was when he found out Frylock was dying of cancer.
Small Name, Big Ego- Shake's entire existence revolves around getting people to think he's the best thing since sliced bread. Never works, 'cause he's a moron.
Only Sane Man - He's basically the only ATHF member who's capable of...anything, really. Meatwad and Shake are too stupid to take care of themselves without Frylock around.
Dumb Is Good: For him, at least, making it more like Dumbest Is Good.
The Kirk: He tries to be the mediator between Shake and Frylock, but he's just too laid back to make much of an impact.
Living Toys: They're not really toys, but he can still talk to them. The others can talk to them in "Shake Like Me". In "Dumber Dolls", Frylock buys him an actual living toy, which turns out to be The Eeyore.
Man Child: He and Frylock basically have a father-son relationship, since Meatwad can't think for himself.
Manipulative Bastard: To Shake. Pretty much the only intelligent things he does is subtle, psychological revenge on Shake.
Only Sane Man: Carl's an ignorant, sex-crazed, lazy bum, and on any other show he'd be the wacky neighbor. But since he lives next to the Aqua Teens, he's the sane one by default.
They Killed Kenny: Carl dies ridiculously often, usually because of something the Aqua Teens did.
The Mooninites
Aliens from the moon that look like they'd be better off in an Atari game.
Expy: Ignignokt and Err have the voices and personalities of Baffler Meal Master Shake and Frylock respectively.
Hot Blooded: Err will attack anything that bothers him, and a lot of things bother him. But he's really small, so it's no big deal.
Humans Are Morons: This is the opinion held by Igignokt and Err, believing that they are superior to all life on Earth in every possible way. Unfortunately, they themselves are not all that smart and are always ultimately shown to be dumber than just about everyone they ever meet on Earth—human, food product, or otherwise.
The Power of Rock: In one episode, they get their hands on the Foreigner Belt—a belt that gives the wearer superpowers based on the band's songs. For example, setting the belt to Cold As Ice gives freezing powers.
Red Oni, Blue Oni: The serene and haughty Ignignokt is blue, while the hyper and aggressive Err is red.
Retr Aux: All moon people are designed to look like 8-bit video game characters. The original plan was to portray them as refugees from a failed Atari game.
Rogues Gallery: They're the most recurring "villains" of the show. Their only real ambition is to rob stores.
Small Name, Big Ego: Ignignokt and Err are always rambling on about how the moon is superior to Earth, but when challenged on it, they can't even explain why.
Easily Thwarted Alien Invasion: In their first appearance, they have no real plan. In the second, they intend to "de-terraform" earth, but again lack a proper plan. In the third, they are literally only stealing the Aqua Teens' cable. Frylock's assessment of them is the current page quote.
Feet of Clay: Oglethorpe is initially described as having invented the Insane-O-Flex in the movie, but this is later disproved.
Running Gag: He always wants to return to his home planet, whether it's Dick Planet, Tooth Planet, or Burger Planet.
Voluntary Shapeshifting: In each of his appearances after "Dickesode", he's modified himself with a different body, changing from a "dick with balls of rage", to a tooth, and then a giant hamburger. He always keeps his face and glasses, though.
Whatever form he's in, he has a Batman Gambit to take over the world, but he really wants to be free from Satan. He still has a diaper, yellow eyes, and a shower cap, though.
Turns out to be a zigzagging trope as Dr Weird then insists Fry is his father, then Walter Melon shows up and says he's all their fathers. By the time their mother, a seven layer burrito, shows up, nobody except Meatwad even cares and the movie goes straight to credits.
Significant Name: Everything that he does is weird, though this could be explained by him living in what once was an insane asylum. His antics include teaching his ass to eat his hand, making love to a lawn mower, sending spiders through the phone lines to telemarketers, tricking Steve into allowing corn to mate with him...twice, using a chain saw to cut off his flesh in order to lose weight, injecting himself with large amounts of barbecue sauce, cutting off his own head so that the blood spraying out of his neck will propel him all the way to Phoenix, asking Steve to agitate a snake coiled up inside his helmet, and much, MUCH more.