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I, Koshi Rikdo hereby give my permission to include a couch gag featuring me at the start of every episode of the Excel Saga anime.
The ending credits to Genshiken show the club members watching an episode of Kujibiki Unbalance in the club room in the immediate aftermath of the episode, featuring some sort of visual reference to the events of the episode.
Appropriately, each episode of the Kujibiki Unbalance TV series ended with a pan across an illustration of the Rikkyoin school campus, also with a visual reference to the events of the episode.
Every chapter of Crimsons starts with a water flea (Daphnia) monologuing about life, the universe and everything and is quickly interrupted by being eaten by a fish.
Every episode of Sister Princess ended with Yamada alone in his apartment watching something on television — usually the fictional Humongous Mecha show Garban — which had a comment relevant to the episode's action.
Any anime subbed by Dattebayo Fansubs frequently has a wry comment at the end of the opening credits. This can range from an in-joke between the Dattebayo production team, to something like "Attempting to unlock bankai in three days can be hazardous to your health."
Sayonara, Zetsubou-Sensei has these in the middle of the openings without animation: Series One has large blocks of text, while Series Two has fanart.
Trigun had scenes from the episode in its opening credits. The initial American DVD release left this out, apparently because the US licensor didn't want to create different English credits for each episode.
The endings of Detective Conan in the original Japanese version included clips from the episode.
Every episode of the first half of Lucky Star ends with the characters doing karaoke versions of various anime theme songs (different each episode). They're always arguing at the same time. The second half of the series has Minoru Shiraishi (the actor, in live-action) singing other random old theme songs a capella. The last one, though...
Played more seriously in Eureka Seven: the way Renton and/or Eureka say "To be continued" ("Tsuzuku" in Japanese) reflects the state of things at the end of the episode. At first, Renton is the only one who says it, Eureka joining in about half way through the series to symbolize their relationship moving forward.
The last scene of Omamori Himari's opening changes from episode to episode. When Rinko goes up to Yuuto's room, she always finds him in bed with one (or more) members of his harem in a compromising position. Megaton Punch ensues.
While not exactly a gag, one of the end credits sequences for the second season focuses on a different one of the 13 squads for each episode.
The final opening has Ichigo's outfits change throughout the arc to reflect how his abilities change in the Fullbring Arc.
The fourth opening, "Tonight Tonight Tonight" features a different pic of a character near the end of the song. It was cut out in the U.S. broadcast only keeping the first one.
Though not exactly a joke, the endings to Axis Powers Hetalia have variations of this. During the second season, the ending song was sung by the character that was the focus of that episode. During the third season, a certain potion of the credits changes to depict either the Allies or Axis Powers standing around a tree, and then focuses in one one of the characters' faces.
In season 5 of Keroro Gunsou, each of the episodes using the thirteenth ending theme, "Bokura no Aikotoba", used different art over the end credits (though all were overlaid with the same animation of the Keroro Platoon clapping along to the music).
Hidamari Sketch x365's opening has several: Miyako eating a different dish in each episode, the scroll on the wall behind her changing, the message Hiro writes on the paper airplane changing, and Yuno's attempt at a group picture getting messed up in different ways.
Durarara!! does this as well, essentially "slipping in" a few seconds of new footage in between a section of the Openings; only carrying over the music until it returned to the stock footage. Used very effectively.