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The Legend of Zelda
The Legend of Zelda: Ocarina of Time has the cutscene of Ganon's Castle collapsing into the ground. It looks less like it's breaking down and more like a toy castle that's sinking into the ground, looking nothing like destruction. The castle looks like it's just folding over, and can be likened to a penis going flaccid.
From Ocarina of Time again you have Ganondorf's last bit of dialogue: "CURSE YOU ZELDA!!! CURSE YOU SAGES!!! CURSE YOU... LINK!!!"
That's if you stuck with the default name. "CURSE YOU ... DUDE!!!"
And then there's the fact that NintendoCapriSun actually lost his voice during that part due to trying to shout the lines in his Ganondorf voice. If you've watched his LP, you'll remember how funny that was every time you watch that scene, making it even more Narmy.
Oh, and if you're one of those people who named themselves "Zelda", to get a scene where Zelda says "Zelda... That name sounds... familiar", you get Ganon cursing out Zelda twice.
And then there's the face he makes as he's saying "CURSE YOU..."
Ganondorf's last bit of the text:
Ganondorf: What a worthless creation that ghost was! I will banish it to the gap between dimensions!!
Sheik getting tossed around like a rag doll in the scene where Kakariko is on fire. It's otherwise a very serious part of the game, but that animation just looks ridiculous.
Twilight Princess again, we get the scene were Ilia regains her memories. With over the top music and Epona doing the "Majestic Horse" pose in the background.
There was actually quite a bit of this in Twilight Princess. The example that comes to mind is the scene (which straddles the line between Narm and Nightmare Fuel) where one of the spirits is warning Link that the fused shadows could corrupt him; it brings to mind cardboard props in a god-awful 3rd-grade school play. Not to mention the moment during said scene where a Link who appears to be suffering from cataracts lets loose The Scream.
The best part? At the end of that scene, a bunch of laughing Ilias start raining from the sky while Link watches on, wearing an expression on his face that clearly shows he's high as a kite.
Several minor scenes suffer from poor animation or unrealistic movements (such as the bizarre way Zelda's sword fell, or the utterly silly stumbling animation of the boss in the Goron Mines.)
Those noises Link makes as he's turning into a wolf for the first time sounds more like he's having sex.
The scene on the bridge where Link's horse rears up while he poses, framed against the setting sun. It comes across as trying too hard to be epic that it comes across as narm.
Midna getting ragdolled into the outer walls of Hyrule Castle by the Fused Shadows (which are way too big for her imp form) stuck around her head happens to look very silly.
Even The Wind Waker, despite the humor relying heavily on slapstick anyway, managed to have a short narm scene in the final boss battle, when Ganondorf attacks Tetra. Upon seeing it, Link snaps into a weird, somewhat angry-ish, facial expression for a split second... It's obviously meant to look badass because now It's Personal, but ended up looking more like Ganondorf just trashed Link's Treehome or something, not like he smacked one of his best friends brutally to the ground.
Zelda's Sparkling Stream of Tears near the end of Spirit Tracks comes off as this to some people. Ironically, she ruined a Tear Jerker scene with it. Fight tears with tears, I'd say...
Also in Skyward Sword, Tentalus' introduction after a rather scary moment of the Sandship being torn to pieces with you inside, you'd be expecting some sort of Bad Ass looking kraken, you get... this◊.
The game opens with a rather horrifying nightmare of Link's, involving what appears to be an enormous mouth in an eyeless face made of black scales. One of the nightmares ends as the creature appears to devour Zelda. The figure from Link's nightmare is a boss later in the game, The Imprisoned. When it appears, it tears itself out of its seal in the earth, and you see its enormous mouth... stood up on a pair of short, stubby legs with goofy, balloon-like "toes". Suddenly, the creature is no longer the supremely evil being it first seemed to be.
Even worse: it falls over if it doesn't have toes. And just wait until it grows its hilariously oversized arms.
The inside of its mouth kind of looks like an anus. You've got a gigantic, armless, stubby-legged, scaly anus roaring at you.
Link's face when he gets a rupoor, as well as the caption. See the Poison Mushroom page image for an example.
There's this one scene where Groose is about to go cry and it plays the saddest violin music that it can manage.