The time where after a long practice with Sawako-sensei, Yui lost her voice. (S1 05 21:19). Thanks to Sawako, she can play and sing at the same time, but strained her voice in the process. Now Mio has to sing. "Do it for Husky Yui!"
The part of episode 5 where the characters start acting like they're in a mystery manga.
This pays dividends in episode 6 where Mio does lead vocals for "Fuwa Fuwa Time" but Yui still provides backup vocals... with her hoarse voice.
Mugi "bargaining" with the music store clerk - who, by the way, recognizes her immediately as the daughter of the shop's owner - to get a discount on the guitar. Lower! (S1 02 18:10)
Sawako-sensei trying to punish Yui by making her wear an embarrassing Santa outfit, only for it to backfire when Yui proves to have no sense of shame. (S1 07 13:50)
From Episode 10 in Season 1:
Yui: "What's that?"
Azusa: "It's a tuner. I use it for tuning my guitar."
Yui: "Oh... so that's a tuner. This is my first time seeing one."
Azusa: "Then how do you tune your guitar?"
Yui: "Just randomly." *strums the guitar, all strings are perfectly in tune*
Azusa: "PERFECT PITCH!? I can't decide if she's amazing or not..."
Jakka jakka jan jan jakka jan! JAKKA JAN! (S2 03 14:00)
Sawako-sensei briefly fantasizes about a masked Ritsu playing epic death metal beats at the foot of the TOWER OF BABEL.
Ritsu eating the receipt in front of Sawako-sensei while the rest of the band chants "Swallow! Swallow!" (S2 02 17:29)
At least equally funny or even funnier is what Yui wanted to do with that wad of cash, in contrast to the others. (Oh, and she even got what she wanted, sort of!)
Another one: Mio finally giving in to Sawa-chan's hobby.
Season 2, Episode 14 In an attempt to get hit in the forehead, Mugi tries stealing the one strawberry atop Mio's slice of cake. Just... watch. (S2 14 19:02) The look on Mio's face is what really made that scene brilliant.
Several moments in episode 18 of season 2, as if the plot for that — Mio and Ritsu trying to play against type — wasn't enough.
Mio's Freak Out! in the beginning, complete with her listing reasons she can't be in the play that get more outlandish with each one, is pretty funny - and then the camera angle changes, revealing that Yui has been holding her arms like a tree the entire time.
Mugi suggests to Mio that she should pretend Ritsu is the only one watching her. Mio looks out at the girls and imagines that they all have Ritsu's face.
"That'd get noisy real fast..."
The show starts off hilariously with the first episode of the first season, when the girls try to convince Yui to join their club. In no time the club room changes into nothing less than a war zone, complete with emotional close-ups of all involved. That scene's punch line ("You guys are really not that great") is very funny as well.
There was also that scene a dozen minutes prior to that when Ritsu asked if The Promise Mio made was a lie. Her response? "That entire flashback is a lie."
And from the same episode, Azusa sounding like all four of her seniors on her way to the club room.
Omochi Race. That is all.
"WAA WA WA"
Azusa imagining herself as club president.
Nodoka stopping Yui from eating a crayon on the first day they met.
Season 1 episode 3. PUNI PUNI!!!.
The whole affair with Yui cutting her bangs. Without a mirror.
The whole exchange between Yui and college K-On member Akira.
On the first day of their senior year, Ui decides to change her hairstyle... to look exactly like Yui. She then plays up the joke by saying that she really is Yui ("I wanted to see Azu-nyan and came here pretending to be Ui!")... and Azusa starts believing her.
Ui regrets doing that when Sawako starts talking to her chest, which Sawako has already noticed is bigger than her older sister's from the first time Ui did that.
Sawako: *staring at Ui's chest* "Oh, hello Ui."
Ui: "Hello to my chest? Please don't talk to my chest..."
The new high school light music club member Okuda somehow makes Yui seem like a genius.
It's discovered that she's been inadvertently giving people parts that require three hands or six fingers to play right. This doesn't stop Ui from playing it perfectly. (No, she does not have six fingers.)
One chapter of the high school spinoff starts with Azusa announcing that she's going to run a tight ship, practice hard, and really impress Yui with how great the new club's band is going to be (now that they have enough members). She then walks into the room to find Sumire in a maid outfit serving tea to Sawako.
NOTHING HAS CHANGED!!
Azusa wants to rub Sumire's head, remembering Mio doing it to her. Unfortunately, not enough words — or too many — slip out, and it backfires...
Azusa: No, not me!
Season 1 Episode 14: Live House has a few moments too.
When required to fill out a lighting-sheet for their performance, none of the members of Houkago Tea Time know anything about actually putting on a show, or what to write in the form. Yui's first thought is... To ask the scariest-looking group present.
Ritsu: "In a way, Yui is the toughest of us all..."