Tooter Shellby in The Snorks can't speak, but only toot out of his snorkel. The other Snorks can't understand him, but some other sealife can.
All adults in the various Peanuts animated specials. (They are also unseen.) They all sound like a muted trombone. This is because they were voiced by a trombonist who was told to mimic the line's delivery with the instrument.
Kenny's mouth is (almost) always covered by his parka, so his speech comes through as muted nonsense. Matt Stone is actually saying lines through his hand, and knowing the context can usually allow you to recognize many of the words. This allows the creators to get through some words that would otherwise be censored. Some of his speech is readable in closed captions. Other times his dialogue consists of verbal gibberish used for comic effect, as a sort of "fill in the blanks" device. Because we rarely hear Kenny's unmuffled voice, the identity of Mysterion is not spoiled early just by hearing his voice, due to the fact that he takes a gruff intonation that clashes with the clean farewell in The Movie.
Timmy can only say his own name and a series of meaningless grunts. This was originally supposed to represent his mental disability. However, in later episodes he occasionally shows understanding of complex situations, and attempts to communicate complicated messages through inflection and gestures.
Man, talkin' bout dang ol' Boomhauer on King of the Hill. Boomhauer's speech actually is decipherable, but his Motor Mouth pacing, array of verbal tics, and thick accent often make it possible only to get the gist of what he's saying. The show often subverts the gag in a variety of ways for comedy:
Sometimes he momentarily becomes completely incomprehensible (except for his usual verbal tics), and for the character he's talking to to act like he just said something profound.
Another gag is for minor characters to not understand him at all, even when he is being relatively clear.
And yet another is for his friends to tell him they can't understand a word he's saying, due to echo, bad phone reception, etc.
One episode featured the four main characters each telling their side of the same story. In Boomhauer's version, he is completely intelligible for the first time, and the other characters all talk with his usual speech patterns.
His mother and younger brother share his unique speech patterns.
Lampshaded in an early episode where Hank makes friends with Willie Nelson; at Nelson's party, we see Boomhauer talking to Bob Dylan, who's just as hard to understand.
Japanese exchange student Toshi on American Dad!. He has accurate subtitles, but his friends always react as if he said something else entirely.
In a similar manner, Papi on The Proud Family speaks only in Spanish, with accurate subtitles about how much he hates Suga Mama.
Mush-Mouth on Fat Albert and the Cosby Kids. Though his speech was simply normal speech with a "buh" added after every vowel, and was thus entirely intelligible i-buf you-buh pai-bud a-butte-buntio-bun.
Parodied on Drawn Together, in which Ling-Ling (a send-up of Pikachu from Pokemon) speaks in badly garbled pseudo-Japanese, called Oriental in one episode; the other characters have to read his subtitles to understand him, when they can at all.
Gibber, one of the air pirates from TaleSpin, would only whisper into the ear of the person he wished to talk to. The audience never heard exactly what he said, only the other's reaction to it.
Likewise, in the Clyde Crashcup shorts on The Alvin Show, Crashcup's assistant Leonardo would only communicate by whispering into Clyde's ear.
He did speak audibly on one occasion, when upset with Clyde, in a sort of whimpering wail, without any real words to it.
Simon on Frisky Dingo, who speaks only in quiet mumbles which the characters in the show can apparently understand but which are incomprehensible to the viewer. On careful examination, it appears that the voice actor simply repeats the same nonsense sentence fragments, such as "When I was seven..." over and over.
When Ben from Ben 10 is in his beastly Wildmutt form, he qualifies. There's nobody who can understand him, though.
Also from Ben 10, the alien bounty hunter Sixsix, who appears in the episodes "Hunted" and "Galactic Enforcers" and the made-for-tv movie Secret of the Omnitrix, speaks an unknown alien language. Those working with him tend to be able to understand him, and it's implied that he's pretty mouthy. Apparently you can avoid Repeating so the Audience Can Hear if no one wants to repeat it.
Lil' Cheney on Lil Bush, he begins all his sentences with rah, rah, rah followed by a random word relating the conversation.
Pretty much every robot in WALL•E either talks in beeps and whirrs or can only say its name plus a couple of extra words. The irony is it surpasses some other cartoons by doing that alone.
The bots gain some tonal expressiveness as the movie goes on. EVE, in particular, starts off sounding very robotic and by the middle of the movie has a recognizably human (if distorted) voice.
Wasabi on Sushi Pack speaks only "mustard", but the other members of the Pack can understand him just fine. Ben, not so much.
On Care Bears: Adventures in Care-a-lot, the robot Wingnut speaks in beeps, whirrs, and clicks, but all the Care Bears are able to understand him. Oddly, his creator, Grizzle, is unable to understand him. In one episode, Wingnut translated for another robot that only spoke in blurps.
H.E.L.P.E.R., the Robot Buddy of The Venture Bros., speaks in a series of frantic beeps, which doesn't seem to impair any of the characters in the show from understanding what he says.
On a couple of occasions H.E.L.P.E.R. has behaved as if everyone has completely misunderstood what he was trying to convey, although, considering the audience, they may have simply ignored his advice and done something stupid anyway.
The Clangers only ever spoke in slide whistle tones, which nevertheless had the rhythms of human speech. This was probably because they did in fact have "lines" (though they were never heard by the audience) and when BBC read that one of them was "Bugger it! The bloody thing's stuck!" they were not amused. Their friends, the Soup Dragon and the Iron Chicken, only spoke in growls and squawks respectively. All of these non-verbal communications were interpreted by The Narrator as necessary.
The title character in Ivor The Engine could only communicate through his organ-pipe whistle. How comprehensible he was varied from episode to episode and character to character, though Jones the Steam seemed able to hold full conversations with him.
Zipper on Chip 'n Dale Rescue Rangers rarely speaks anything the viewer can understand due to his often fast and very high-pitched voice (the high pitch being appropriate for him being a fly). The other Rescue Rangers all seem to be able to understand him to some degree, although Monterey Jack is really the only one who seems to be able to understand him perfectly.
Donald Duck himself is difficult (but possible) to understand most of the time, and goes full-on unintelligible when angered enough. One short had him completely unintelligible all the time until he swallowed special pills (which temporarily gave him a normal human voice.)
If one were to slow down their dialogue, they speak very clearly; it's worth noting that until 1950, all of their dialogue was repeated from their first episode "Private Pluto".
The eponymous character of the Canadian cartoon Kevin Spencer apparently does speak, and the other characters around him react as if he had actually said something, but the audience never hears his voice. Instead, the show's voice-over narrator tells us what Kevin "says."
The Looney Tunes' Tasmanian Devil, with several notable exceptions ("What for you bury me in the cold, cold ground?"). In the spinoff series Taz-mania, his family seems to understand his growls and gibbers just fine.
There's also Buster/Shorty from the short "Rabbit's Kin", his high pitched sped up voice makes it difficult to understand what he is trying to say, however, if you were to play it in slowmotion you can understand him perfectly.
The Godpigeon in the "Goodfeathers" shorts on Animaniacs spoke in such an impossible mumble (an extreme parody of Marlon Brando as Don Corleone) that he had to be translated by his associates. The one time he was subtitled, the pigeon he was talking to completely misunderstood him. (He thought he was being given romantic advice; the Godpigeon really just wanted to go get pasta.)
There was also an episode of Pinky and the Brain where there were two old fellows, one of which understood the other's incoherent rambling.
"Yes, yes, I know, I know, but where on earth are we going to find a duck and a hose at this hour?"
The World Leader in The Secret Show speaks in an unintelligible gargle that only her husband can understand — he translates for both the viewers and the other characters.
Recurring character, Monsieur Meccaneux the mechanic in Victor And Hugo has a great line in rambling Yorkshire-ese which is often met with mute imcomprehension by the brothers.
All dogs in The Mighty B! are The Unintelligible. This wouldn't normally be worth noting, except for the fact that they're the kind that the other characters can understand fine, just not the audience.
Gary, Spongebob's pet snail from SpongeBob SquarePants, can only communicate through meows, but everyone understands him just fine.
Except at one point where his response to one of Spongebob's borderline insane ideas is, "Ehh, NO."
Spongebob: Oh what do you know? You're a snail!
And when Spongebob was able to visit Gary's dream, revealing the snail's true loquacious nature.
Grubber of the Gangreen Gang in The Powerpuff Girls, who communicates purely in raspberries. Despite this, he can still imitate people's voices flawlessly and once demonstrated that if he stands up straight he speaks clearly (and generally looks less weird).
In reality, if one listens to the General carefully, they can tell he is actually just talking very fast.
Rufflefeather from the "Go Go Gophers" segments of Underdog speaks a fictitious American Indian language. It doesn't offer much variety to the phonemes; in fact, if Runningboard didn't understand him, we might assume that he just sputters insanely. This is ironic, because Rufflefeather is The Smart Guy who comes up with most of their plans to screw up the cavalry.
Fiskerton of The Secret Saturdays speaks in a series of grunts and mumbles. According to the series creator, his voice actor has a script of what he would say in English, but translates it to 'Fisk-speak'. Fisk does have bits of easily intelligible speech mixed in with the gibberish (most notably, his catchphrase, "Say what?"), though.
One of the members of Lars' clique in Rocket Power, though Lars seemed to be able to understand him perfectly.
The (very un-P.C.) animated adaptation of Dick Tracy from 1961 had, of course, Mumbles. His partner in crime, Stooge Villa, was the only character (or at least, only other gangster) that could understand him.
One episode of The Simpsons had Homer telling Marge something in a panic.
In Yellow Submarine, Old Fred tries to get the Beatles to help him, but his agitation has his entreaty to each of them coming out in frantic, unintelligible gibberish, always ending in "...BLUE MEANIEEEES!!!" (which, by the time they get to George, Ringo and John have joined in).
James William Bottomtooth III, James William Bottomtooth VI and Virgil Mastercard from Family Guy.
Peter's brewery co-worker, Opie, speaks in complete gibberish that the audience can't understand, but everyone else can understand him perfectly.
Rico from The Penguins of Madagascar to an extent. Although as the series progresses, his vocabulary increases to occasionally include intelligible phrases and words besides "Ka-boom!"
The Adults in Ed, Edd n Eddy, any time we hear them "speaking", it is usually garbled mumbling or sound effects.
The villains of the pilot episode of The Tick, the Idea Men, could not be understood because the helmets they wore muffled their voices too much. They had to wave a sign with their ransom demands in front of a camera in order to get The City to understand what they wanted.
In Transformers Prime, Bumblebee does not speak, presumably for similar reasons as his movie counterpart. He communicates by way of electronic beeps a la R2-D2, and is understood just fine by his fellow Cybertronians, but can't use human speech. Raf Esquivel can understand him anyway, and as of the end of season one, the reason for this remains unknown. Even he has said he doesn't know why he can understand 'Bee.
This gets plot relevance later on when It exposes the fake Optimus Prime, who can't understand a word he's saying.Not that it helped much.
Without a Universal Translator Mustache, the alien Meap from the Phineas and Ferb episode "The Chronicles of Meap" can only say the word "meap", which is utterly meaningless to English speakers. To be fair, though, it's evidently a legitimate language amongst his species, where the single word contains implausibly high amounts of context and nuance. To illustrate, in "Meapless in Seattle", Meap has to warn his home planet that the villain, Mitch, had obtained the source of Cutonium and was returning with it to their home planet with the intent to take it over, and as such to ready the armies for war. Trying to explain the situation in English to another fellow alien only gets a confused "meap?" in response; taking off the translator mustache and uttering a single "meap", however, gets all of that across instantly.
In "Tri-Stone Area", the entire cast is turned into this, since the episode revolves around caveman versions of the main characters who spend the episode speaking in a nigh-incomprehensible caveman language (with the only english coming from the photo-animation cutways that feature the animators explaining what's going on).
Pinkie Pie become this in the My Little Pony: Friendship Is Magic episode "Bridle Gossip" when her tongue swells up after walking through the poison joke. When the main cast goes to confront Zecora, thinking she caused the various problems they're suffering with a curse, and Pinkie wants to sing her song about Zecora again, she briefly tries, before begging Fluttershy to do so. Fluttershy agrees, not sounding thrilled about the idea.
In Tom and Jerry: Shiver Me Whiskers, the red and blue pirates speak in variations of "Argh" while their parrots translate for them. However, the purple pirate speaks normally and it's his parrot who speaks in "Argh".