Expected in Azumanga Daioh as it's based on a manga that makes great use of Beat Panels, but the anime shows an amazing talent to not only use a lot of them, but also make them actually extremely long, to the point that they start to become even more funnier once they are way beyond the point where the jokes should have become overdone. Osaka and Tomo produce most of them, but also Chiyo and Sakaki have a number of their own.
The chronological last episode of the anime's first season has a very extensive (almost three and a half minutes!) scene featuring nothing but Yuki quietly reading as the sound of people from other classrooms shouting Japanese pop-culture references fills the background.
Season 2 takes this further with eight episodes, each titled simply Endless Eight. These episodes are a "Groundhog Day" Loop where the characters are trapped in an endless summer. In the novel, we see only one iteration: the last. In the adaptation, however, they break from the source material by putting in one episode where they don't discover the loop, making it seem like a simple summer-y Slice of Life episode Haruhi style to viewers not familiar with the original, and not one, but six where they do realize the loop but do not escape. And then one more where they do escape, making a round eight episodes. Despite the Internet Backdraft and unauthorized professional apologies (among Seiyuu and a dissenting and fired director) that resulted, the arc is distinguished as a rare overly long gag that spans multiple HOURS. Unfortunately the arc was so poorly received that it ended up being the Franchise Killer.
"By the way, which end is the head of a chocolate cornet?"
Hiyori and Konata try one of these in the manga, and Konata (naturally) takes it too far, prompting Hiyori to tell her, "You can stop saying that now."
The trope is actually parodied and lampshaded between a conversation of Miyuki and Tsukasa on the very first episode, going for about 40 seconds before it cuts to Kagami, crying, thinking in her thoughts for the conversation to end with a punchline.
Potemayo does this in episode 4, with the titular moeblob getting a cold and repeatedly blowing her nose faster and faster until she eventually runs out of tissues.
One episode of Cromartie High School takes this and runs it into the ground, with Hayashida trying to remember the name of a song he heard Mechazawa humming. Most of the episode is the students humming while trying to remember the name of the song.
In the Dragon Ball GT special, Goku's spirit does it when seeing Goku Jr., saying that the kid must be his "great-great-great-great...Oh, you know what!"
Hayate the Combat Butler has an overly long gag made of...overly long gags at the end of episode 16. Five minutes of random characters not actually doing anything for about a minute each, or Klaus doing something boring.
Axis Powers Hetalia has the repeated "Wok-fu on the Beach" scene, which has been used in so many different ways and always ends up being interrupted by some out-of-the-box figure, from a Singing Grandpa Rome to Santa Claus Finland.
Episode 101 of Inazuma Eleven has Saginuma's ridiculously long letter to Inazuma Japan, which consists mostly of Endou's unintelligible fast-forwarded chipmunk voice and that alone lasts for more than 20 seconds, while the whole scene takes almost a minute.
Jungle de Ikou!, when Mii rhetorically ask why an American plane is flying above them at that moment, except she adds the specs for the plane mid-sentence. (That is, she lists the plane's size, weight, crew capacity, and so on in the middle of the question).
A filler episode in One Piece prior to the Impel Down Arc had Franky shaking his speedo-clad manly bits in the center of the screen for what seemed like several minutes. "Right! Left! Right! Left! Right! Left! Right! Left! Right! Left! Right! Left!"
Also in the anime is Amazon Lily's inhabitants' individual reaction shots to getting hit with a reverse-Bridge drop. All twenty-plus of them.
There was one in Sanji's fight with Mr. 2 Bon Kurei, who has the power to copy anyone's appearance. Bon Kurei performs his Mane Mane Montage, which is supposed to turn his face in a montage of the weirdest faces he's seen. When he finishes, his face remains UNCHANGED except for his nose, which is now Usopp's (long) nose. There was then an awkward moment of silence that was like, twenty seconds; shortening that was one of the few good things that 4Kids, the company whose purpose is to Bowdlerise anime, did to One Piece.
Akumetsu chapter 22 contains 2.5 pages with panels containing some variation of "we cannot show you the lyrics here".
At the end of one episode of Legendz, one of the minor characters is seen putting on his clothes again. Then, as he's got one arm in a jacket sleeve, the secretary comes in behind him and tells him he's fired. They stand there while the full opening instrumental of the ending theme plays, him occasionally blinking, expressions unchanging, and arm still in sleeve. Not a single word from him, no further words from her. It just keeps going through to the credits.
To apologize (and for laughs), they give you a stinger that has a more-proper reaction from him.
One episode of Nichijou had a scene where Yukko is hit on the head by her teacher. This is then shown over and over again, from different angles and with different background colours for almost a minute straight. The funniest part about it is the noise she makes, and hearing it over and over again.
Episode 5 of Haiyore! Nyarko-san W opens with Nyarko and Cuuko playing cards while Mahiro's mother uses an alien vacuum cleaner (basically, an excuse to have repeated cries of "Cyclone!" "Joker!"), until it gets on Mahiro's nerves and he sucks the cards up in the vacuum. The gag is repeated at the start of Episode 9, with Mahiro even lampshading the déjà vu, but it quickly gets interrupted by Hasta. There are two points to the gag, however; one, both episodes in question focus on Cuuko's Clingy Jealous Girl cousin Cuune, and two, it sets up a subversion of Chekhov's Gun at the end of the latter episode where Mahiro and Nyarko both remark that, with all the attention it got, they expected the vacuum to be more relevant to the plot.