The OAV series Tenchi Muyo! (not to mention the spinoffs and sequels), has plenty of moments.
From the first episode, Tenchi's "Oh Crap" reaction when he breaks his ancestor's (really his grandfather's) sword, which breaks the rock that sealed the chamber where Ryoko was imprisoned. Made funnier in the English dub once Tenchi realizes the true impact of his blunder:
Tenchi: I'm giving these keys back to grandpa and do as many chores as he says!
Tenchi: Huh? (grabs his groin) No way! They're mine, and I'm gonna hang on to them!
Ryoko: Oh, you numbskull, I meant the jewels on your sword!
In episode 4 (one of two Hot Springs Episodes), Noboyuki attempts to get Tenchi to peep on the girls. He's trying to be all sneaky and everything... until he looks up and sees Ryoko looking over nonchalantly and freaking Noboyuki out.
A few moments after that, Tenchi's broken away from the feuding Ryoko and Ayeka to recover, only to have Sasami spot him. Seeing his state, she only has one thing to say: "You're a naughty boy, aren't you, Tenchi?"
The aftermath of the Single-Stroke Battle between Tenchi and Kagato. Tenchi wins however Kagato's spaceship Soja is ALSO cut in half as well.
Just about the entirety of episode 7, but the ending deserves special mention. Ryoko and Ayeka attempt to get Tenchi all to themselves by sending Mihoshi back to Galaxy Police HQ and locking Washu in her lab, then setting up a trap on Tenchi's door that sends anyone who passes through it into the lake outside. However, Sasami defeats the trap by simply... walking through it slowly, ignoring Ryoko and Ayeka's fighting, telling Tenchi about a really bad dream she just had. Ryoko and Ayeka can also hear Washu inside, so they try to rush in through the door, and get sent into the lake. To top off their Humiliation Conga, Mihoshi returns from Galaxy Police HQ, and crashes her ship on top of them. Seeing as how Ryoko and Ayeka are both Made of Iron, they naturally survive, but the looks on their faces just before the ship crashes are priceless.
Actually, all you have to do to get by the trap is to knock on the door. Ayeka said Ryoko had no manners because she didn't knock. Sasami knocked on the door and was allowed to go through. Besides, Tenchi was the one to open the door anyway.
Episode 8 has Washu reveal her past... then attempt to win Tenchi over using her rarely-used adult form!
Ryoko and Ayeka's exhausted chants of diapers and milk, with the latter eventually drinking out of the baby's bottle.
One part of episode 9 has Tenchi, Noboyuki and Katsuhito fixing up the roof of the hot springs they wrecked. Noboyuki accidentally smashes his thumb with his hammer, leading to Katsuhito chastising him... before smashing his own thumb. When Tenchi calls them boneheads, Katsuhito's able to distract Tenchi long enough to have him smash HIS thumb.
Katsuhito:Now who's the bonehead?
At the end of the episode, even Tsunami could not get a word in on a Ryoko / Ayeka argument. It's not often that you get to tell a goddess to shut up / stay out of this.
The entire scene after Misaki arrives for the first time in the OVA. Gets Turned Up to Eleven after Ayeka's, "My mommy!"
Ayeka even warns Ryoko not to laugh, or she'll be sorry. Ryoko laughs anyway (complete with Face Fault), and comes face-to-face with Misaki in Mama Bear mode.
Most of episode 13 qualifies, particularly everything after the Emperor of Jurai's arrival: The entire Royal Family (including Tenchi) seems to await his arrival with the appropriate amount of respect - until he does arrive: The Emperor is pretty much The Comically Serious: his demands for his daughters to return with him to Jurai are ignored, particularly Ayeka due to her constant bickering with Ryoko over Tenchi. Even raising his voice didn't get Ayeka's attention. Even Sasami said she'd never forgive him if she's made to leave Earth. Even Ryo-Okhi's dance in child form to him to make him happy has him initially utterly perplexed until the former starts crying. Funaho comforts Ryo-Ohki, while giving him a look that says "you're being a jerk". Really, the guy completely came off as the No Respect Guy in that episode. Ironic given his status.