Banjo-Kazooie: Both Mumbo Jumbo and Humba Wumba, in addition to a few side characters, in this series. Rather jarring in Wumba's case, being a heavily stereotypical Native American in a game released in 2000.
City of Heroes: The Trolls are a gang whose members take a drug that gives super-strength but mutates them into giving them their distinctive troll-like appearance; it also apparently causes their brains to degrade to the point they start speaking like this. Ironically, this is the only effect (well, that and rage issues) Superadine has on the brain. Trolls are still as intelligent as anyone else; it's just the language centers that are affected.
Not necessarily. With any foreign ethnic group you can find plenty of people with thick accents or grammar quirks and plenty of people without. Thrawn could simply have a better command of Basic than the the bartender, being much more highly educated and erudite, as well as a definite Omniglot.
Diablo: "We strong! We kill all with big magic!" The poor little demon had obtained a tavern sign depicting a sun and naturally expected it to be magical.
Dungeons & Dragons Online: Kobolds, Orcs, and other monstrous races vary in their eloquence. Sometimes this can be written off as different tribes having different levels of understanding of Common, but other times it's jarring when two members of the same group or even the same individual switches depending on which stock quote they use.
Etrian Odyssey III: The Drowned City: The barmaid speaks this way. It's surprisingly cute.
Fallout 3: Has the Super Mutants. Player characters with low Intelligence also talk this way.
Also exhibited with the Ronso. It's kind of hinted that this is merely a language barrier, since the Ronso Maester speaks perfectly eloquently, but Kimahri has spent at least ten years away from Mt. Gagazet and still hasn't learned a personal pronoun...
Final Fantasy XI: Has the majority of the beastmen use simpler forms of the Five Races language, if at all. Goblins and Lamia are actually more fluent in the player's language, although for Goblins, being good at language is good for business. It's also subverted in that there's a very well-spoken Orc in Wings of The Goddess, as said Orc is actually a cursed Elvaan. Why is this text spoiler'd and not the earlier part? Because it's actually an aversion; the Orc is really a well-learned Genre SavvyMagnificent Bastardreal Orc who puts this trope and the expectations of it to work in order to trick you into freeing him, and it's only until you meet him again in The Lost Woods that it's revealed you've been had.
This series by Spiderweb Software features a race of creations called Serviles, which are designed to be human-like enough to serve as a general slave race (menial workers, assistants in offices, blacksmiths, etc.) but are kept dumb enough to prevent independent thought and ultimately rebellion. One effect of this is that they speak in very simple English.
In the first game, serviles are abandoned on an island and develop their own cultures. Despite significant advances, two of the three factions deliberately continue to speak in simplified speech. The Obeyers, who do so because they know the Shapers wanted it, and the Takers, who hate the Shapers and would rather speak like Serviles than like Shapers. Only the Awakened, who believe in equality between Shapers and creations, speak proper English.
Homeworld: Cataclysm: The Beast starts by speaking in broken English, and has an...idiosyncratic method of speech when controlled by the player. However, as the campaign goes on and the Beast adapts and learns, it finally speaks to the captain as an equal.
While proper English is almost always much-lauded, one well-known player character named Bashy often talks like this, which is then lampshaded in various in-game items. Still, his vocabulary is far superior to what it seems at first glance; as for his excuse for speaking like that, he claims it to be an artifact of his Prussian upbringing.
The goblin minions in the GameInformPowerDailyPro Dungeon talk like this, to which your character tries to protest "No, that's kobolds..."
The Legend of Dragoon: Kongol speaks this way, never using pronouns if he can avoid it. What makes the whole thing so strange is that Kongol was raised by humans, but his brother who only lived with others of his species speaks with a perfectly normal syntax.
Possibly justified in that a normal Vorcha lifespan is twenty years.
Twenty years assuming they don't get killed. Though they regenerate insanely fast (on higher difficulties, a headshot is the only thing that is guaranteed to kill them immediately. Everything else can be healed in about three to five seconds), their culture is based on injuring each other to become stronger. Because they regenerate so quickly, being injured actually makes them stronger. Their culture has a lot of murder, according to the Codex.
Salarian doctor Mordin Solus. Subversion of trope. Salarians have short lifespans. Fewer words means more time. Also speak very fast.
In Mass Effect 3 however, Shepard does meet some Vorcha who actually speak in complete sentences.
The kobolds in this series. Actually, being Dungeons & Dragons Kobolds, they're as intelligent as a human, and have a developed, if exceptionally violent, culture. Their poor language stems from their typical genocidal hatred of anything except dragons and other kobolds; they consider Common beneath them and don't bother to learn to speak it properly. A sample line from Neverwinter Nights 2 (where orcs also speak a form of You No Take Candle):
Deekin: Yes, Deekin very kobold, last Deekin look in mirror. Deekin not do that much; mirrors usually too high for Deekin.
The first game also has an Ogre Mage who has a sarcastic retort to a player character who observes that he's very well spoken for an ogre.
Pokemon Vietnamese Crystal: This very poorly translated bootleg version of Pokemon Crystal, is practically made of this trope. Everyone in the game has appalling grammar.
Re VOLUTION: There is quite a bit of broken English in this game. The company FUN Labs is Romanian, so they might not have native English speakers on hand.
Rumble Roses: In the English language version, Aigle, the Mongolian girl, speaks like this.
Runescape: The Ogres speak a vaguely Jamaican accent, which is commented on multiple times. Some Ogres that have lived with humans speak grammatically correct, albeit short, sentences. They still use lots of slang, making some sentences almost unreadable. The goblins, though speak in a 'stupid' way with incorrect grammar. In an inversion of this trope, they are revealed to be very smart, but most tribes of goblins care more about warfare and physical strength than science, art, and intellectuality.
planetmind speaks variously broken English, but is a vast planetary intelligence into which humanity may eventually merge.
This is a bit of an oversimplification; it turns out the Alien Kudzu is actually a vast neural network that self-organizes into a god-like mind, but in doing so destroys its necessary supporting organisms and dies back down, only to repeat the cycle in a series of tragedies. Humanity is able to break the cycle. So initially, Planet Mind is not very bright, but it just keeps growing...
Sunset Riders: The third boss, Dark Horse, who rides a dark horse covered in plate armor, introduces himself with, "You in big heap trouble!" When you defeat him, it turns into, "Me in big heap trouble!" The sixth boss, Chief Scalpem, talks like this, too; he shouts, "Me ready for powwow!" when you meet him, and "Me powwowed out!" when you take him out.
Pagan: I hearsy, I hearsy, and you should be afearsy (When you provoke them into searching for you.)
Pagan 2: I be leaving a letter for that thiever, Garrett.
Pagan 3: I be want to be deading him, not leavings him letters.
Pagan 2: Me too. But Dyan saying hims might be beings useful to us.
Pagan 3: Thinks you hes be reading it?
It is suggested that some of them are perfectly capable of speaking proper English, but choose to speak in that mangled way deliberately. It's certainly true of their god, The Trickster, who generally speaks the same way, but is perfectly erudite in his speech when posing as the nobleman Constantine.
Gargoyles in this series aren't excessive users of this trope, but have one very notable trait: they use "to be" for all forms of "to be".
To be thinking that an example to be needed to explain. To be of the mind that the effect to be lost by your description. To know that all sentences to be of a personal nature. To explain that at first only winged gargoyles to speak, but later all gargoyles to speak. To not know why this to be.
In other words, gargoyles have no subject phrases—only predicates—and they do not conjugate verbs. Also, every sentence is implied to be spoken of oneself.
Also, the passive voice is spoken in by Emps in Ultima VII.
In Ultima Underworld, The Stygian Abyss, the goblins are a perfect example for this (especially the Green Goblins except for their king). Try to trade with one of them and make an offer he rejects. The answer: "No, I no like!"
Vandal Hearts 2: Your hero will - after a Time Skip - pick up two faithful allies. One of them is a guy known as 'Vlad the Ox' who speaks like this, when not devolving all the way down to Hulk Speak. Naturally, everyone - including your other ally - assumes that he's simply Dumb Muscle... which he finds really annoying since, as he soon reveals, he is simply a forreigner who did not start learning the local language until a few years ago. In truth, he's both quite wise and clever. Mostly noteable due to this trope being directly adressed by him.
In this video game series, the "primitive" language is actually named "Low Common" in Warcraft DnD - implicitly there's a "low" form of many other languages, as well. World of Warcraft actually subverts this at one point:
Draz'Zilb: Why the puzzled stare, <name>? Expecting me to speak like an uncouth ruffian merely because I am an ogre?
Most of the time though, ogres are more like this:
Ogre: What ecology mean? Me smash you!
One of the classic battle cries of kobolds is "You no take candle!". Incidentally, kobolds are one of very few races depicted as almost universally stupid. Later lampshaded/parodied by the mushroom-stealing ogres of Zangarmarsh, who sometimes shout "You no take mushroom!" Oddly, the phrase isn't echoed by the snobolds of Northrend.
This has become such a recognized line among the fanbase that the novel Stormrage has kobolds shouting this in a dream sequence, with another character responding "I-don't-want-your-damn-CANDLE!"
Also parodied in a later quest where you have to catch Kobolds with a net. One of the possible responses from the Kolbolds is "You no take... me!"
For those who don't know, kobolds put burning candles on their heads presumably to function as a miner's light even when they aren't in a mine.
However, if you spend time around one of their above-ground lairs in Loch Modan, you can overhear a kobold practicing archery—and remarking on his accuracy in crystal-clear Common.
Further subverted in a Northrend questline where the player learns the tongue of the local murlocs. Murlocs are always portrayed as not terribly bright and their gorloc cousins speak in pretty broken English, but in their own language, the murlocs are actually surprisingly erudite. (And there's even a gorloc who's learned better Common and speaks both perfectly and intelligently.)
"Before you say anything, do not assume me as foolish as most of the Gorlocs you've met. I've been into the world a bit, I've learned your language, and I'm not easily duped." The implication isn't that he thinks the other Gorlocs are foolish, but that you might think them foolish because of their not good speaking and funny acting. Their leader in particular can say quite philosophical things and catch and eat shiny bugs at same time.
A Justified example is the wolvar (wolverine-people) of Northrend, who point out once or twice that there is no real reason for them to know Common/Orcish or how to write. For instance, on a "Wanted" notice board in Zul'Drak:
Chief Rageclaw sorry for bad writing. First time use one of these things; plus, Chief Rageclaw is wolvar, not person.
That said, they're also consistently portrayed as not very intelligent creatures, all told. One of the Frenzyheart hunters who accompany you on quests in Schalozar Basin thinks he has to tell you that you aren't a wolvar. Their speech also delves into Hulk Speak territory; they know of gorlocs, but only refer to them as "big-tongues." Of course, the gorlocs call them "puppy-men."
Furbolgs (humanoid bears) are another interesting case as most of them are encountered as enemies apparently incapable of speech, but the few of them that are willing to talk to you all speak in a rather sophisticated manner.
Starting off as a Draenei gives you a possibility to take a quest line where you actually learn to read/understand Furbolg, for the duration of the quest. And then, in the same way dropping a proficiency makes you weaker, you forget you ever knew Furbolgish, and they only roar at you from then on.
In the case of the Furbolgs it's justified in that the ones you talk intelligently to are how all Furbolgs used to be, and the brutish, animalistic ones are those that had been driven mad by the invasion of the Burning Legion during Warcraft III
Many of the uncorrupted Furbolgs are allies to the Night Elves, who can speak coherently. Unfortunately, almost all of these specific Furbolgs are corrupted.
You later encounter the Timbermaw Furbolgs, whose slightly broken Common/Orcish (depending on which side you play) sounds rather more like lack of language fluency than lack of sophistication.
From Warcraft III itself, you have the trolls, at least in the French translation. With the notable exception of witch doctors, who talk sophisticated instead.
In Mists of Pandaria we meet the Virmen, rabbit-like creatures who are obsessed with vegetables in general and carrots in particular. "You no take carrot! You take turnip instead!"
There are also Hozen, Monkey-men who pepper in common with words they seem to have made up themselves, they're only unintelligable until you figure out what means what ("wikkets" means outsider, for example). Justified by them only having a life expectancy of 15 years, well-learned Hozen are extremely rare, even if they're an elder. A few speak in more complete sentences, such as Tak-tak, a kite-glider pilot for the Horde, who transports Horde players to various locations for the Dominance Offensive quests and will comment on the questline's events during flight.
One hozen, Mokimo the Strong, speaks as eloquently as any human, tauren, or Pandaren, likely due to the fact that he's a member of the Golden Lotus, a group made up primarily of Pandaren.
Xenoblade Chronicles: The entire Nopon race speaks like this. They are fond of this way of speaking, and say that the Nopon that try to speak correctly like the other races are just trying too hard to be cool.