Couch gag
Generally, between one-half and two-thirds of the couch gags used in a season are new, while the remaining couch gags are repeats. Most couch gags are used at least twice, with a second occurrence usually in the same season as the first. Most of these are Halloween episodes. Furthermore, The Simpsons Movie does not feature a couch gag in the opening, however there is a couch gag-like scene during Homer's vision.
History
The first episode of the series to air, "Simpsons Roasting on an Open Fire" (episode 7G08), didn't feature a couch gag. The second episode (aired and produced), "Bart the Genius," features the first couch gag to be aired. When the family sits down on the couch, Bart is squeezed off the couch and pops up into the air. During the shot of the television set following the couch shot Bart is seen falling back down in front of the TV. This is one of the few couch gags that continue into the closing shot of the TV.
Extra long couch gags
The most-used couch gag in first-run primetime airings, first used in "Lisa's First Word," involves the family forming a chorus line with a group of dancers. The living room background makes way to reveal [unicyclists and elephants in a large production number. Used a total of eight times to date, this extra-long couch gag has mostly been used when episodes were in danger of being too short. The extra length of the gag would compensate for the shorter episode. This has become less common in more recent seasons, as the required length for each episode has been reduced due to additional advertising.
Another extra-long couch gag is when the family tries to sit on the couch, but it tries to attack them. Other couches attack people (though Moe is able to fight them off by shooting them with his shotgun), with the closing scene as Homer going into a couch store, sitting down, and being attacked. This couch gag was first seen on "Marge's Son Poisoning", then rerun on the season seventeen finale "Marge and Homer Turn a Couple Play".
The season 18 episode, "Homerazzi", has what is now the longest couch gag to date (beating out the Powers of Ten parody seen on "The Ziff Who Came to Dinner" and rerun, with different dialogue, on "On a Clear Day I Can't See My Sister" and "Eternal Moonshine of the Simpson Mind" by 45 seconds), where Homer goes through evolution, starting out as a unicellular being and dividing rapidly until he becomes a jellyfish, then a common fish (that almost gets captured by an octopus that looks like Mr. Burns) until he becomes a prehistoric lizard that evolves into a rat and nearly gets attacked by a T-Rex who looks like Bart but is stopped by a stegosaurus that looks like Lisa. After surviving the meteor crash that kills the dinosaurs, Homer then evolves into different types of monkeys as he goes through a jungle, then becomes more human as an Ice Age occurs, transforming from a Neanderthal, to a Cro-Magnon, and finally to an upright-walking caveman. Moe Szyslak (also a caveman) passes by Homer with a brief "Hey" and devolves into a ratlike mammal. As Homer continues walking, he evolves into men from different historical eras (nomad in the Middle Ages, Spanish explorer, Pilgrim, and Victorian-era intellectual) until he finally evolves into his modern self and comes home to the rest of the family. Marge asks Homer, "What took you so long?" (when this couch gag reran on the season 19 episode "The Homer of Seville", Marge's last line was changed to "Did you bring the milk?") and Homer sighs in exhaustion.
Other couch gags
One of the most memorable couch gags involved the Simpsons arriving to find The Flintstones sitting on the couch. It was first featured in the season four episode "Kamp Krusty", but was later used in repeat airings (and in international airings) of "The Itchy & Scratchy & Poochie Show" (which originally used the couch gag from "Bart After Dark" where the living room is a detailed replica of the Beatles "Sgt. Pepper" album, featuring every character and object from the show and statues of the Simpsons as they were on the Tracy Ullman Show cartoon shorts) to commemorate the show beating the The Flintstones' 166-episode mark as America's longest-running animated prime-time sitcom.
A reference to another show by Matt Groening, Futurama, was made in the couch gag for the season 12 episode "HOMR" where the family is deposited on the couch via the travel tubes that appear in New New York City, but Fry comes down the chute instead of Bart (which is quickly corrected when Fry gets sucked up and Bart comes down).
For the season 19 premiere, "He Loves to Fly and He D'ohs" the entire theme song was modified as a callback to The Simpsons Movie. The couch gag featured the family running in to see Spiderpig sitting on the couch. Homer lovingly picks up the pig and says, "My summer love."