Subverted lately in that characters have come to learn 'Bizarro Speak' as a recognized language. Bizarro isn't stupid, just complicated (and homicidal).
Extremely complicated as it's practically impossible to say which parts of the phrase are to be inverted or misconjugated. He says the opposite of what he means, but Depending on the Writer, that would mean "You no am Superman" could mean "You are Superman," "I am not Superman," or "I am Superman," or even "I am Bizarro" (because Bizarro is the opposite of Superman, you'd expect him to switch their names.) And since even the comic has more than one version of the character, it can even mean "you are not Superman."
In the Justice League Unlimited episode "The Great Brain Robbery", Bizarro is the only member of the Legion to figure out that the guy claiming to be Lex Luthor wasn't Lex Luthor. However, telling everyone... that's a different story.
"Ever since you use brain machine, you am acting perfectly sane and rational... am you Bizarro's mommy?"note Bizarro was originally created by Luthor in an attempt to create a loyal Superman clone
The Incredible Hulk, though he doesn't do as much talking as most other incarnations. Count on at least one of the people he's trying to "Hulk Smash" at the moment to tell him third-person speaking is a sign of conceit.
The DC Animated Universe version of Solomon Grundy (who at first glance seems a Captain Ersatz of the Hulk, complete with "Grundy crush!" replacing "Hulk smash!") talks in Hulk-speak but is capable of full sentences.
Miek from the Planet Hulk storyline; Though strictly speaking he actually doesn't speak English and his speech is just translated by Sakaaran talkboxes, he can't seem to grasp verb conjugation at all; "is [verb]ing" is the form he uses for pretty much every verb in every context. In general, his lack of aptitude for speech is implied to be due to his people not naturally communicating verbally, but by "chemming".
Note that his original toy lists his intelligence as a 7 out of 10 (compared to poor Sludge's 3), decently above-average.
To put this in perspective, if Optimus Prime is sidelined, Grimlock's generally accepted as the next most-capable leader in the good guys, across almost all media in which he appears. Someone else got the job in the movie, and gets gunned down in the next fight, while Grimlock isn't only the most prominent old school survivor in the movie, he led an army in revolution in a subplot.
Played straight in Y: The Last Man: Natalya Zamyatin is a Russian secret agent whose English is described as being "beyond broken", making her sound somewhat stupid. However, whenever she has a chance to speak in Russian, she waxes loquacious. While not explicitly Lampshaded, she is well aware of the overall effect.
Natalya (in Russian): "<Thank Christ! I sound like a retard when I try to speak English!>"
Agent 355 (an American, also speaking Russian): "<Slow down. Who is you?>"
In the epilogue, decades later, one character remarks on meeting Natalya and being impressed with her excellent English. An older character who knew her during this time laughs at this.
Subverted in the post-Zero Hour Legion of Super-Heroes with Chameleon, who starts out speaking none of the language the other characters use, and spends quite a while gradually learning the language and speaking it very brokenly... right up until the payoff of an Arc which reveals, among other things, that he's been perfectly fluent for quite a while and was simply concealing it so that nobody would suspect him of impersonating certain key figures.
Corollary: Starfire of DC Comics can leap over the whole hurdle of communication by kissing someone to learn their language. Any brief physical contact will do, but kissing is the method she prefers.
Vlad in Hack/Slash talks in broken English, thanks to being brought up in isolation by a reclusive Czech-American butcher who didn't speak English very well.
In later Thunderbolts comics, the Black Widow speaks English this way, until it's revealed she's actually Natasha Romanova impersonating Yelena Bolova, and consequently imitating her comparatively lacking grasp of the English language.
In the revamped Guardians of the Galaxy, a telepathic Russian dog named Cosmo conveys his thoughts to others in a thick Russian accent, despite the fact that Cosmo is only directing his thoughts, and can convey them to people perfectly no matter what language they speak.
In Final Crisis, Superman notes that Overman speaks English this way because on his world (where the Nazis won World War II because they had the most powerful superheroes on their side) it's a dead language that he only knows due to his top notch education; he's never had occasion to speak it before, so he speaks it slowly and carefully enunciates every word.
Cleaner Slugs from Green Lantern comics are used by other species as literal organic garbage disposals. They'd probably get more respect if they could use pronouns.
Krypto the Superdog, in a sort of meta-example, has his thoughts presented to the reader this way to emphasize the difference between the thought processes and language uses of dogs and humans.
Similarly, Dex-Starr from the Red Lantern Corps in the Green Lantern comics does this for the same reasons, although his thoughts are usually verbalized by his ring.
Ting-a-Ling, the Polynesian Stunt-Girl from Jet Dream and Her Stunt-Girl Counterspies, has this speech pattern in early stories, but speaks perfectly fluent and colloquial American English in her last Character Focus story.
Mek-Quake from 2000 AD. He also talks in the third person and makes, often pointless, declarative statements for further emphasis, along with a frequent cry of the catchphrase 'BIG JOBS!'. It is not an accident he also happens to be a massive robot Bulldozer.
In the Astérix album Obelix and Co., this is how Caius Preposterous talks to people who didn't study economics ("'If you not able make big heap menhirs, me not able pay big heap sestertii"). This leads Obelix to conclude that this is how businessmen talk, and soon everyone's doing it.
In Violine, Kombo, an African witch doctor, tends to talk like this.