Elective Unintelligible - Television Tropes & Idioms

This character is The Unintelligible by choice, for many reasons, such as Obfuscating Stupidity. He may require Translator Microbes or a Translator Buddy most of the time. When he speaks comprehensibly, it usually means something important.

Examples:

Mumbles from Dick Tracy. Only after enduring questioning under the lights for a time (and a specific threat from Tracy) does he suddenly speak clearly, "Eighty-eight Keys set you up. Big Boy paid him to get you out of the way."
Fenster from The Usual Suspects, played by Benicio del Toro. He chews up his words so badly sometimes even his Heterosexual Life Partner can't understand him.
The two jailers from Monty Python's Life of Brian. The one played by Terry Gilliam speaks utter nonsense and the other (Eric Idle) has a severe stutter that causes him to draw out almost everything he says. These seem like verbal tics up until their last scene, where, after everyone else had left, they start speaking perfectly clear to each other, implying that it was all just an act to keep people from pestering them.
In the film version of The Little Rascals, "Uh-huh" is so named because that's all he ever says. At the end of the film he instead says "Uh-uh", causing the other Rascals to react with shock that he learned a new word. Uh-Huh immediately responds "Actually, I've always had a rather extensive vocabulary, not to mention a phenomenal grasp of grammar and a superlative command of syntax. I simply chose not to employ them".
Pikeys in Snatch.

Rebo and Zooty are a comedy duo from the fictional universe of Babylon 5. Zooty speaks through some kind of electronic device as part of the comedy. Rebo claims that in all their time together, Zooty has only ever said one thing to him out of character: "Why?" Before leaving the Station, Zooty tells President Sheridan, "Because it tells me to." Notable in that Rebo and Zooty were played, respectively, by the boisterous Penn and the silent Teller.
A famous sketch on The Benny Hill Show has Nicholas Parsons playing an interviewer talking to Hill, playing someone with a very heavy accent—e.g., Chinese, French, shanty Irish. Parsons has to keep asking the interviewee to repeat himself every other sentence because what he [Hill] says is incomprehensible, and frequently sounds off-color. In another sketch, Hill plays a fumbling Dutchman who uses his inability to speak the language to chat up an attractive woman he meets in the park. It turns out he's faking it and speaks perfect English.

BIONICLE: Turaga Nuju, who uses the bird language. He had Matoro as his Translator Buddy.
- The Vahki could actually speak the Matoran language, although too was high pitched for others to listen.

Pete in Darths & Droids took "mute" as a disadvantage in order to improve his stats, and must talk in beeps when speaking in character. Fortunately, nobody ever speaks in character, so this isn't much of a downside.
The Order of the Stick has Blackwing, Vaarsuvius' raven familiar. Blackwing can speak Common, but considers it demeaning to speak anything but his native raven language. To Vaarsuvius, anyway. Later, once V thanks Blackwing for his noble efforts and starts treating him like a sentient being, Blackwing starts talking.

Taz in Taz-Mania, though he usually spit-growls incoherently, can speak perfectly well if need be, or if it's funny. On one occasion, all he had to say was simply "Taz hate water", but chose instead to give a long-winded speech. It wasn't received well.
Nibbler on Futurama. Mostly just makes strange, gibberish noises... until The Reveal.
Grubber, one of the Gangrene Gang on The Powerpuff Girls, often speaks merely via raspberry-ing, which no one outside the Gangrene Gang seems to be able to understand, but in the Gang's premiere episode, he speaks eloquently (in a Bad Bad Acting kind of way) in order to lure Blossom and Bubbles into a trap. In another episode, for show-and-tell at the Powerpuff's school, he stretches his body into a more normal shape, and greets the class with "Hello, I'm Grubber. Very nice to meet you all." Before changing instantly back into his usual shape.
In Hanna-Barbera's version of The Little Rascals, Porky does speak English, but only when he and Buckwheat are alone. For instance, this exchange from "Wash and Werewolf":
Porky: Darla gonna be mad!
Buckwheat: You took the words right out of my mouth.
In American Dad!, Toshi understands English perfectly fine, but refuses to speak anything other than Japanese out of nationalistic pride.