There are subjectives, and then there are these. While you may believe a work fits here, and you might be right, people tend to have rather vocal, differing opinions about this subject. Please keep these off of the work's page.
Neon Genesis Evangelion
An important note here: Neon Genesis Evangelion has some of the most subjective narm in anime. The difference between a scene being hilarious and horrifying is very small, and sometimes divisive. At certain points things can be so over the top that they somehow cross the line twice and turn back to serious/horrible, perhaps more than once (the infamous "mind rape" scene can be seen as this by some). This can happen at any point in the scene and naturally can be the difference between hailing it as a masterpiece and hating it.
Generally speaking, while the Evangelion dub contains a number of truly outstanding performances and scenes, it also "balances" this by also having a greater-than-average number of Narmy hiccups. How greatly the positive aspects outweigh the negative tends to be a matter of personal preference, and is the main reason for the dub's Love It or Hate It status among Eva fans.
A more specific example: the single frame held for about two minutes in episode 24 is meant to be a dramatic scene in which Shinji is realizing that he has no choice except to kill his new buddy. The scene is held so long that the audience is likely to forget what they're watching and why, or even wonder if there's a problem with their TV when watching it for the first time. AMV Hell 2 mocked the crap out of it.
To make it worse, this sort of animation fail happened several times during the series.
Similar to episode 24 above, the elevator scene with Asuka and Rei is held still for so long, it becomes silly.
However, in the Director's Cut, Asuka is animated to have several subtle facial expressions play across her face as her frustration builds like steam pressure in the water heater the MythBusters tested to destruction, which changes the scene from narmy to genuinely compelling.
The infamous moment at the very end of the TV series: Shinji's revelation, which takes about a minute, ends with everyone clapping and cheering "Congratulations!" The only thing missing is that it wasn't a slow clap.
Every time Shinji yelled "Ayanami!" quickly. This was mostly done in episode six, and it makes the final battle scene hilarious.
The way Shinji shouts "Misato-san" can be inadvertently hilarious, as well. "MISATO-SAGHN!"
After a while, the sheer number of mental problems the cast has becomes funny — especially Ristuko's relationship with Gendo, which involves an insanely hot scientist being treated like complete shit by a balding ugly dude who spends most of the series in only one pose. This adds special meaning to "dysfunctional."
Several of the musical pieces have cheesy English lyrics. "Showdown", "Keep Your Head Above the Mayhem", and "Fate" are examples.
The opening scene has Shinji and Misato survive a blast of the N2 mine. It sends their car flipping, but neither of them are injured even though neither of them were wearing a seatbelt.
The crappy (lack of) animation made episodes 25 and 26 amusing to some people.
The scene in episode 9 where Asuka and Shinji train for an upcoming battle by doing synchronized DDR.
There's also the part where they both brush their teeth, spit into the sink, and then growl at each other like they're getting ready to compete in some epic teeth brushing contest.
This episode seemed to be intentionally comedic, so these events are likely outright jokes and not narm.
In one of the earlier episodes, Shinji is sitting in a movie theater, and we see a close up of his face with blank, bored looking eyes. It cuts to a shot of two people making out in the seat in front of him, and then back to Shinji, whose eyes then quickly accumulate a gratuitous amount of "shinies," making him look like he just morphed into a chibi.
Another English dub example: Ritsuko's (Sue Ulu) breakdown in episode 23 flirts with Chewing the Scenery, particularly her delivery of this line:
"... NOT EVEN WHEN YOU MAKE LOVE TO MEEEE!!!!"
Japanese dub, Asuka struggling to speak German — the character's native language. In the English dub, the German is solid, since Tiffany Grant speaks German fluently.
So fluently, in fact, that she also voiced Asuka for the German dub.
Ladies and gentlemen, the English dub of Episode 13.
Shigeru Aoba: Intruder is accessing the main security banks... it's cracking the passcode! Twelfth digit... sixteenth digit... it's in!
In episode 22, Asuka flirts with Kaji and when he rejects her she screams "I'm an adult! So look at me!" while pulling her blouse apart and shoving her breasts in his face.
Fuyutsuki's Dull Surprise often becomes funny. Memorable lines include: "Sweet Jesus, it's an Anti-AT Field." and "Oh dear God in Heaven, SEELE has delivered an angel to us." Exactly in the tone you'd expect Dull Surprise to fall under.
The ending theme of "Fly Me To The Moon" can be downright hilarious coming directly after tense cliffhanger endings.
End of Evangelion
Misato killing the soldiers that tried to kill Shinji in End of Evangelion becomes hilarious in the English dub because of the cartoonish sound effect added when she shoots one in the head. It sounds like someone squeezing a piece of slime. That same sound effect was used almost as inappropriately during Instrumentality.
There's another narm-y bit in the English dub of the movie: when the JSSDF is raiding NERV headquarters, one soldier fires a flamethrower down a hallway twice. The dub adds someone saying "Hit 'em again!" before the soldier fires the flamethrower a second time.
Funnily enough, both this and the previous example involved, you guessed it, everyone's favourite dub-director, Amanda Winn Lee!
Asuka's expression right before a (fake?) Lance of Longinus breaks through her Eva's AT Field to stab it (and her) in the eye.
Being reduced to LCL is accompanied by an audible "pop." And the LCL looks like orange soda/banana pudding/Tang.
The song played during End Of Evangelion as humanity's souls are turned to LCL just screams Soundtrack Dissonance- it's WAY too jovial for the situation here.
End Of Evangelion: Makoto Hyuga's voice actor being replaced by a freaking black man who sounds nothing like the original actor becomes the single-most jarring moment to a viewer who watched the anime from start to finish.
The worst delivery probably comes when the NERV staff is in panic and Maya is crying asking if there is a way they can escape. The response? "HOW THE HELL SHOULD I KNOW?"
Fuyutsuki's English voice actor underacts dear god. "Sweet Jesus. It's a giant AT Field."
Rebuild of Evangelion
From the second film; in the Zeruel battle, Zeruel eats Unit 00, leaving nothing but ankles spraying blood. With Shinji watching this, this is chilling... until Zeruel comically spits 00's head out.
Another example is this completely serious exchange between Rei and Gendo:
Rei: Commander... Do you find meals enjoyable?
Rei: And do you find pleasure in eating with others?
Rei: And the act of cooking, that's enjoyable, isn't it?