In the "Saving Private Brian" episode, Stewie warns Brian, "You can't run away from the Army. They'll come after you, like Peter went after that hockey coach." After a pause: "What, no clip? Thought we had a clip."
In another episode, when Peter launches himself with a catapult. We get a scene of a man in a room, going over a list of all the precious, easily breakable things that are in that room (including a hemophiliac baby). Of course, Peter lands... right outside the window to the room, and proclaims "Those are all nice things!"
A more classic example happens when Peter tries to deviate a parade to his house for Stewie's birthday party. He waits ahead at a fork for the parade to come holding a Detour sign... then he slams it on the parade leader's head, knocks him out, steals his uniform and leads the parade to his house.
In the episode "Brothers and Sisters", Mayor West tells Carol he has aides, leading Carol to think West meant the STD. West points to two men that are his aides and then says they have AIDS.
There's another episode where Adam West is looking for a sign to warn people about his ferocious dog. You would think he's looking at the "Beware of Dog" sign, but he's actually looking at the "One Way" sign, so that people will know that there's only one way they can go to get away from his dog.
In one episode, Brian confesses to Peter that he's in love with Lois. Peter looks at him and says, "Oh my God!" Then he pauses and adds in: "You can talk!"
In a Cutaway Gag, Peter thinks back to when he was potty trained. The flashback starts by showing Peter as a kid, but the camera zooms out revealing it was only a picture showing a full-grown Peter running up to Lois saying, "Lois, I did it!"
In the episode where the Griffins have a reality show set up in their house, Peter speaks to the executive producer and says, "This is what I think of your contract!" As he says this, he holds the contract as if he's going to tear it in half, but he doesn't. He just sets it down and says that he thinks the contract is stupid.
Towards the end of the episode, "Pick Up Your Ears", Lois tries to think of a way to get into Chris' school, which she had been banned from, and the school is safely guarded by security. Naturally, Peter has a plan. Cut to a very tall man in an overcoat, who's head clearly looks like Peter's and legs look like Lois', but then the camera cuts back to show Peter and Lois still hiding behind the bush. Peter says that guy in the overcoat is large enough for them to get behind him and sneak in.
In another Cutaway Gag, Peter places a dollar on the ground underneath an anvil he is hanging by a rope in a tree, he waits to drop it on someone who picks up the dollar, but only seconds later, he falls for his own trick by saying, "Ooh, a dollar!" and going after it only to smash himself.
In an earlier episode, there's a Cutaway Gag where Peter cuts a cake but ends up accidentally slicing a woman inside the cake (who was supposed to surprise the guests by jumping out of it). Peter yells, "Ah, crap!" but not because he killed the woman; it was because the cake was coconut flavor.
The episode, "Killer Queen", has a Running Gag where Brian comes up with many creative ways to get Stewie to see the giant robot on the cover of Queen's News of the World album, which scares him to death. At one point, Stewie walks into his room and sees an unopened Jack-in-the-box. At this point, Stewie thinks he's onto Brian thinking the robot will pop out. He turns the crank anyway, and it turns out to be just a normal clown. Stewie sighs of relief, but turns around only to see the robot on his wall!
When Peter comes across his old bicycle, he remembers how much fun he had with it when he was a kid. Cut to a young Peter having a tea party with his bike.