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.
At least for its first 33 episodes Happiness Charge Pretty Cure will have cameos of each of the previous Pretty Cure heroines up to that point congratulating the franchise for hitting 10 years.
The Queen's Blade second season closing credits play a musical number featuring one of the Swap Witch Trio (Menace, Airi, Melona), changing each episode.
The preview for the next episode of Koufuku Graffiti always does things that took place within that episode.
In episode 1, Kirin and Ryou simply sing the tune and spin in conjunction with it.
In episode 2, Shiina, who was introduced in the episode, joins the two girls.
During episode 3, the character from the movie the girls watched in the episode spins around with food on his head and hands. Ryou watches in suspense to see if he drops the plates.
In episode 4, the shopkeeper in that episode notices a young Ryou unable to choose between two items. He then does a little hand movement to distract her.
In episode 5, Shiina's mother dances to the song. Shiina then draws her mother, who then goes over to look at her drawing.
In episode 6, Kirin sings and dances like in episode 1, though in a towel, while a nervous Ryou hides just offscreen. Kirin pulls out a popsicle to draw her out, but Ryou's towel comes off just as she jumps for it. Kirin then jumps in front to block viewers from seeing Ryou naked.
During episode 7, Kirin and Shiina do the singing/dancing, while Tsuyuko stands in the middle. She pulls a fan out and spins with the girls right before it ends, with Shiina's mother popping out at the last second to record it.
In episode 8, Kirin and Ryou are running, and attempt to spin during that section of the song. Ryou however, is unable to keep up, and gradually falls behind, but still attempts to do the spin during the appropriate time. However, due to her exhaustion, she's off by a second.
In episode 9, Akira, Ryou's aunt, and Kirin's mother take over the dancing portion. Kirin and Ryou just watch them until the very end, when they join in on the spin as well.
In episode 10, it starts with Kirin and Ryou as back in the first episode, but then the camera starts panning lower, as if to go into Yuki's apartment which is below Ryou's. Yuki watches them, and attempts to dance, but is too shy to do much. Kirin then pops her head down, and both she and Ryou jump down and spin her briefly towards the ending of the preview.
In episode 11, Kirin, Ryou, Shiina, and Yuki all sing and dance together. Shiina starts dancing a brief moment after Ryou and Kirin, while Yuki starts shortly after Shiina does. Despite that they spin in unison during the appropriate sections of the song.
During the Journey into Tama arc, Tama was replaced in the credits by a pixelized version of herself.
For a time, part of the credits of Yu-Gi-Oh! 5D's played over a still image of Yusei holding a card. The card itself was always prominently featured in the episode.
The ending theme for  always — except for the first episode and the OVA "Ankou War!" — follows the same template: after a few seconds of sun, a close-up of the front of a tank's side as it moves forward toward the left of the screen; then a shot of it moving along a path, pointing diagonally with respect to the screen, and with its operators in super-deformed form sticking out of the tank; then a side view of same, then a front view of same, then the show logo in the grass. The differences are in which tank and who the operators are. Understandably, the Anglerfish Team's Panzer IV shows up a few different episodes, always reflecting its current setup: when Saori changes to communications, she starts wearing a headset in the ending theme; when the IV gets a barrel upgrade, that shows up, too; when it gets its Schürzen skirts, those, too, are shown.
The ending theme of Shinryaku! Ika Musume's first season is nearly always set at the beach at night, usually with Squid Girl looking out over the sea, and even the exception ends that way. But then, there's always something referring to one of the mini-episodes, such as fireworks, or the oversized Squid girl head, or the mini-Squid Girls walking by.
At the end of Please Tell Me! Galko-chan's opening segment there are some introduction about the main trio, which is different for each episode. This comes from the manga, where the character bios for the characters are different for each chapter and are customized for each chapter's content.