Though it's primarily and generally Peter and his knee. This gag is often modified, by having another character be the one hurting their knee or another part of their body.
Peter receives the last silver scroll in a bottle of Pawtucket Patriot Ale and someone tells him to run home as fast as he can. Peter does just that, a la Charlie from Willy Wonka & the Chocolate Factory to the music of "I Got a Golden Ticket". When he finally gets to his house, he trips over himself and hurts his knee. He spends a really long amount of time wincing in pain afterwards.
Later on, in the same episode, after being banned from the tour of the Pawtucket Brewery, Peter asks Pawtucket Pat if he even gets a Chumbawumbas song. Pat obliges, but the Chumbawumbas only sing part of the song before kicking Peter in the knee, causing him to do this gag again. Only the very beginning of this gag is shown, before cutting to the next scene.
Peter goes on a job hunt and his laziness, stupidity, and incompetence gets a job as a public school gym coach. When he works his job, he screams at the kids to do the obstacle course faster and stop being so lazy. Peter gets sick of the kids messing up and one of the annoyed kids challenges him to run the obstacle course himself if he's so smart. Peter assures him that he doesn't need to because he's the teacher and the kids says that he's so fat, that he'll probably be terrible at it. This calls Peter's bluff and he accepts the challenge. However, as Peter walks over the the obstacle course, he trips and falls and hurts his knee before he can even start. Peter spends a long time hissing and moaning in pain, as the kids mock him for his lousiness. This exhibition of incompetence gets Peter fired almost immediately.
Peter drinks while driving and then a cop pulls him over and does a drug test on him. He asks Peter to step out of the car and walk in a straight line. Peter does just that and walks in a perfectly straight line ... into the streets. Peter walks through quick, oncoming traffic and just narrowly avoids getting hit by cars without even noticing what he's doing. Mr. Magoo watches this and admires Peter's ability to absent-mindedly avoid traffic with such persistence. As he does, he loses concentration of his own crossing of the street and gets himself hit by a car and killed. Peter finally makes it past all the traffic with flying colors but when he does, he trips over the curb and hits his knee on the sidewalk on the other side. In great pain, Peter grasps his knee and once more, heavily breathes in pain for a ridiculously long time.
Lois comes down to the docks to see Peter partying with his friends, when he should be at family game night. She gets pissed, screams at him a little, and then kicks him in the shin before leaving, leading Peter to drop to the ground and enact this gag.
In opening credits for the new incarnation of The A Team, Peter plays John "Hannibal" Smith. In the theme sequence, his Jeep runs over him and he grabs his knee, and begins wincing in pain.
Lois is now the victim. After signing a contract with Fox News Channel, her boss tells her to run home as fast as she can, but she trips. Unlike Peter's initial trip, she actually grabs hold of her boob.
A snowspeeder ropes an Imperial AT-AT Walker by the legs, and the walker falls. After getting up grabs its "knee" and begins wincing in "pain".
The British version of Peter "Neville" falls down and grabs his knee, hissing "bugger" through the pain after being chased Benny Hill-style by the London Bobbies for accidentally killing Queen Elizabeth II.