In a strange in-joke, there's a "cursor" pun in The Muppet CD-Rom: Muppets Inside, which features a Whatnot wandering past the Databus, muttering "Ahh, the dirty little frazbasset grummelslinger, the little shrooby rooby..."
Murray in Sly 2: Band of Thieves. The combination of spice and hypno-boxes slowly made this happen, until he mindlessly roared and charged at Sly.
Team Fortress 2: In the "Meet The Spy" video, this is the BLU Scout's reaction to seeing pictures of the RED Spy with his mother. Or rather, this is the RED Spy's (actual) reaction to seeing that the BLU Spy got hold of pictures of him with his "petit chou-fleur". Or both.
Kirby Super StarUltra. Revenge of Meta Knight. Heavy Lobster. Paint Ability. When you hit Heavy Lobster with it, its entire body gets covered in paint and its eyes stop working, causing it to flail around erratically. The crew of the Halberd subsequently break into angrish trying to comprehend how easily Kirby destroyed the giant shrimp mech.
Captain Vul: Rassa frassa blassa! Arrrgh!
In Kirby Star Allies, when you knock off Hyness' hood, he loses it so completely that he goes into this.
Mitsunari from Sengoku Basara is usually pretty good at coming up with gruesome and imaginative death threats, however when enraged his inspiration fails him and he starts yelling "I'LL KILL YOU!" over and over again.
The Anger Sphere from Portal doesn't speak, instead it only growls at the player.
Marie from Persona 4Golden tends to run words together rapidly whenever flustered, embarrassed, or upset; for example: "stupidjerkfaceihateyou." Did we mention that she's a Tsundere?
In the Thief games, if you are being chased by a guard and you climb or jump to somewhere they can't follow, their immediate response is pure, incoherent Angrish in frustration at you escaping.
In Mass Effect, when Saren hears Shepard made it to the beacon on Eden Prime, he freaks out, stomping around the control room and sputtering incoherently. It's actually Sovereign that's pissed off, and acting through Saren, but has the same effect.
Saren (subtitles): Argh! Grr! Rahr!
Decidedly not played for comedy in Asura's Wrath. When Asura gets mad (and we mean truly mad, as in transforming into Berserker and Wrath modes), he can't form coherent sentences and expresses himself through pure murder and violence. Also inverted in the first DLC episode; when Chakravartin kidnaps Mithra, Asura flies into Wrath mode, where he was previously unable to speak, but he manages to form a few coherent sentences when speaking to Mithra while trying to bash through the barrier holding her.
In Borderlands, using Brick's Action Skill, "Berserk", will sometimes cause him to scream incoherently as he rushes toward his enemies, punching them. The same goes for Krieg in the second game, whose dialog is generally a mix of this and nonsensical phrases involving meat or blood.
Inverted in Borderlands 2 in the case of the Goliaths, who upgrade from Hulk Speak and actually become more eloquent and...vivid as they're consumed by their rage once you knock their helmets off. They're still sputtering fountains of rage, but they can at least speak complete sentences at that point.
Earthworm Jim; Jim does this if you lose one of between-level races with Psy-Crow (which means you have to fight him before proceeding to the next level), and also at the Game Over screen.
In Commander Keen 1 there are several martian churches, where you can receive telepathic messages from the saints. In one of the churches the saint is a Garg (a species of martians consisting of a large mouth with eyestalks, who hate basically everything) and the telepathic message is: YOU HEAR IN YOUR MIND: GAAARRRRRGG!
In Danganronpa: Trigger Happy Havoc, when Makoto Naegi, the protagonist, manages to figure out who the first culprit is, the first culprit freaks out and starts screaming "AHO AHO AHO AHO AHO AHO AHO!" repeatedly, which translates approximately into, "RETARDED RETARDED RETARDED RETARDED RETARDED RETARDED RETARDED!" The official English dub changed this into "STUPID STUPID STUPID STUPID STUPID!".
In the sequel, the first culprit falls victim to a different kind of Angrish, where he lapses into a country accent (Cajun in the dub) so thick that the other characters can't understand him, forcing them to rely on Monomi as a translator.
One of the early missions with Trevor in Grand Theft Auto V involves him becoming so angry most of his dialogue consists solely of "AAAARRRGH!" and variations thereof.
In Bravely Default whenever Edea gets especially angry her sentences can be either be preceded or followed by "Mrgrgr!" to the point that it almost doubles as a verbal tic.
Pester the Grox too much in Spore and they scream at you.
All of Hothead's title cards in Speed Runners are unintelligible anger.
Cantr II: A favoured tactic of some players when their character is having a bad day. Yelling "RRRRRRRGGGH! You insulted Moss", is a timetested tactic of the type.
In Medieval Cop 6: Dregg Me to Hell Dr. Sigh sends Dregg to a "resort" which actually is an insane asylum.
Dregg: Why that gomaosmdosd..... I am gonna dwoaosasa...!!!
Fallout: New Vegas: Yes Man is programmed to always find the bright side in what you're doing, always agree and find you are correct every time, in order to both be as helpful as possible and boost your ego (the programmer did it for himself, but he got killed and forgot to make sure Yes Man didn't do that for everyone he met). So when you do something that is both utterly detrimental to your cause and completely fucking stupid, he is literally at a loss of words and stumbles a lot on his own speech for a good bit until he can finally find something his programming will allow, and even that sounds completely sarcastic (he supposedly can't get over how "brave" you are, to make things so challenging to yourself).
In the South Africa zone of The Secret World, John, a.k.a. the disembodied Black Signal becomes incandescent with rage while talking to you on the phone, resulting in his speech becoming unintelligible static for a few seconds.
In Persona 5, a target that's under the Rage status effect (increased melee damage but decreased defense, can't take any actions but melee attacks against a random enemy) will do nothing but howl death threats over and over.