You've heard it a million times. A character will open his mouth to speak, and the minute he does you immediately know that this character is stupid. Whether he's an over-muscled Mook or the Plucky Comic Relief, the one thing you can tell just by his voice is the fact that his elevator just doesn't go all the way to the top floor.
Very common in animated works, because allegedly such an obvious characterization tool appeals to children. In The Golden Age of Animation, this sort of voice was used a lot by characters who were a parody of Lenny from the film adaptation of Of Mice and Men.
When the character is male, generally expect a halting voice in the low registers, or else a high-pitched quavering, with most sentences beginning with the word 'duh'. When the character is female, expect a high-pitched nasally whine or an even higher-pitched squeak-fest. Often, characters with this voice will use poor grammar. Male characters often substitute the t or d sounds for the th sound, like saying "dat" for "that." A Valley Girl accent helps for female ditzes.
A very common characteristic of Mooks and The Ditz.
The French dub of Dragon Ball Z is notable for giving an extraordinarily nasal voice to Vegeta of all people. It's been theorized that not having read the entire story, the voice actors had originally expected him to be a generic cartoon villain, and thus gave him a generic cartoon villain voice; cueHeel-Face Turn...
It was never a "moron" voice though, more of a "evil schemer with permanent Psychotic Smirk" voice.
Recoome of the Ginyu Force; the "dumb-as-nails Psychopathic Manchild" vs "hammy sadist who's just toying with you" ratio depends on who's voicing him.
Moose from Archie Comics is written this way. He used to say "Duh-" before every line.
The Ogrons in Doctor Who should be this, with one exception. In Day of the Daleks, the Controller confronts two Ogrons. The first one says, "We found...and destroyed...the enemy." The controller asks if there were any complications, and the second one replies, "No complications," in a perfectly normal voice.
Subverted in Big Bang Theory: Bernadette speaks with a high, nasal, squeaky Dumb Blonde voice, but has a doctorate in Microbiology.
Booji Boy, mascot of Music/Devo , a character portrayed by their singer Mark Mothersbaugh in a baby mask. Booji Boy exemplifies the band's philosophy of Devolution, and talks with a squeaky voice, known for such phrases as "We're all Devo".
In Bells Are Ringing, Ella adopts a "dumb chorus girl" voice during "Just In Time" when an audience gathers to watches her dance with Jeff, but goes back to singing in a normal voice before the song ends. (This was another role originated by Judy Holliday.)
In "Buddy's Blues" from Follies, the "Margie" and "Sally" caricatures talk this way.
Boastful: While elcor from Mass Effect have this tone of voice down to a T with the low, "drooping" pitch and lazy inflection, they avert this trope by being as intelligent as any other species and sometimes prone to Spock Speak to make up for the lack of emotion in their voices.
Goliaths in Borderlands 2, the Giant Mook enemy type of the Bandits. Strangely, their speech is a lot less slurred when you make them angry.
Strong Mad from Homestar Runner speaks in an extremely exaggerated version of this trope, Played for Laughs. Most of his dialogue is nigh-unintelligible growls, but if you listen closely he is saying actual words...probably. Homestar Runner himself is a (somewhat) more subdued version of this trope.
The voice of the Wii in thisDreamcast vs Wii video.
Hyuck! Goofy (1932), first appearing in the early days of the sound era, may have been the very first cartoon character with a voice like this. Bill Farmer is capable of pulling off the voice while still giving Goofy an impressive emotional range in modern productions.
Homer Simpson is the leader of a small crowd of such characters from The Simpsons.
Quite ironically, Ralph Wiggum, a character well-known for being unintelligent, is an aversion of this trope. His voice is high-pitched because he's a child, not because he's dumb, and it is no higher than the other characters who are children.
Parodied/subverted with Oxford "Ox" Haas, one of the soldiers Grampa Simpson served with in World War II in "The Curse of the Flying Hellfish." He spoke with this voice, and looked exactly like the kind of person who would.
Burns: How many of you are familiar with the concept of a "Tontine"? (Beat; all stare at Burns silently, until Ox raises his hand). Burns: All right, Ox. Why don't you take us through it? Ox: Duh, essentially, we all enter into a contract whereby the last surviving participant becomes the sole possessor of...all them purty pictures.
In one Imagine Spot where Lisa imagines her future after losing her intelligence, she's inexplicably gained a southern accent.
Also Beaky Buzzard, and Junior from the Three Bears shorts.
Mugsy of Rocky and Mugsy
The identically-sounding Runt and Ralph from Animaniacs.
Various minor Ren and Stimpy characters, such as Lump and Loaf. Not to mention Stimpy himself.
Chris Griffin from Family Guy. This wasn't actually the intention; Seth Green went into the audition and decided to do his impression of Ted Levine as Buffalo Bill in Silence of the Lambs as a joke, but ended up getting the part. Inevitably, this is referenced in a cut-away gag where Chris does an impression of Buffalo Bill dancing naked (and tucked back) in front of a mirror.
And in the original version of the Pilot, his voice is more of a typical low-pitched simpleton voice.
For that matter, Barry in American Dad!!, who has the same voice.
Derpy is a strange case; Tabitha St. Germain was, apparently, under the impression that Derpy was meant to be a boy. So Derpy was never actually intended to have this trope; she just got one because Tabitha isn't very good at Crossdressing Voices.
Actor Bill Fagerbakke (who is quite intelligent, urbane, and friendly in person) has made a career out of this trope. In addition to voicing Patrick Star in SpongeBob SquarePants, Broadway in Gargoyles and Bulkhead in Transformers Animated, Fagerbakke played Tom Cullen in the miniseries adaptation of Stephen King's The Stand and Dauber on Coach; all of them had the "big dumb doofus" form of this trope.
Karl Pilkington of The Ricky Gervais Show and An Idiot Abroad sounds notably less intelligent than Ricky and Steve...naturally, he is.
He is intelligent enough sounding for a working class guy from Manchester though.
Studies done on rural American Accents found that a disproportionate amount of preschoolers who spoke with vernacular rural accents (Vermont, Appalachia, etc.) were placed in special education classes for it.