Assassin's Creed: Rogue Arguably multiple examples but a particularly jarring one is the main character Shay Patrick Cormac. Voice actor Steven Piovesan is a Canadian and his Irish accent is at times painfully bad.
Wolf O'Donnell in Star Fox 64 speaks with a faux English accent until in his death throes drops it for an American one to say "No way! I don't believe it!"
Similarly, in Star Fox Adventures, the American-sounding Fox has a tendency to lapse into British pronounciations of words. In the scene where he talks to Belina after rescuing her from the mines, Fox completely loses any traces of an American accent. It's just for a few lines, but still!
In the second Ace Attorney game, when you meet the defendant of the third case, a very flamboyant and vain circus performer named Maximillion Galactica, he doesn't really grasp that he's been arrested and is on trial for murder. Once you seriously spell it out for him, he begins frantically speaking in a frantic country bumpkin accent, revealing himself to be a hillbilly who's actual name is Billy Bob Johns. After he calms down, he speaks normally again.
Most of the supposedly American characters in Heavy Rain are played by French actors and it shows, as they slip constantly, especially for Ethan Mars.
Even worse are the kids, whose accents fall into What the Hell Is That Accent? category and whose lines are oftentimes incomprehensible were it not for the subtitles.
Norman Jayden's voice and motion capture actor, Leon Ockenden, is from the U.K., but attempts to go for a New England accent with his character. Needless to say, it doesn't sound very convincing.
When Ethan screams for his son JASON!, it sounds more like he's yelling JAAAY-SUNG!
Played with in Guild Wars. During EotN's hero tutorial, Budol Ironfist states that he'll try to speak like a human (as opposed to the standard scottish dwarf accent). He continually lapses back into dwarf speech.
T.T. in Diddy Kong Racing is supposed to have an American accent, but traces of his voice actor's native British accent keep slipping in and out depending on the voice line.
The Irish Clover Bartender from Toonstruck constantly switched from an Irish to a Scottish accent, Flux Wildly points this out.
That was actually an aversion of both this trope, and the Scot Ireland trope. Notice he's wearing a kilt, too; his accent ping-pongs back and forth because he's half Scottish, half Irish.
In Elder Scrolls IV: Oblivion, a beggar with a raspy voice might suddenly perk up when you ask them about the weather. This is because only lines unique to the beggars (like asking for and receiving alms) were recorded with the "beggar voice." For any lines they share with non-beggars, like a generic response to requests for information, they simply use the normal townsperson voice.
A rare text example of this trope comes in the French localization of Pokémon Sun and Moon and its Alternate Universe version, Pokémon Ultra Sun and Ultra Moon. In most versions of the game, Kahuna Hapu speaks in a very formal, almost Antiquated Linguistics style of speech. In the French localization, Hapu (called Paulie in the French localization) speaks much less formally and is instead given something akin to a Québécois accent, with words like "moi" and "toi" rendered as "moué" and "toué." However, this is not consistent and some other lines of hers have her use the standard "pronunciation."
The voice actress for the protagonist of A Vampyre Story tries to mix a French accent with a Transylvanian one. Not surprisingly, her success is mixed as well, though she does a better job of it than you might expect.
Mark Meer (the voice actor for male Shepard) is Canadian. He does his best to sound completely neutral in regards to accent, but it does slip through from time to time (most noticeably when saying "been" with a long E sound).
Canadian voice actor John Ulyatt does a decent Scottish accent as Engineer Kenneth Donnelly in Mass Effect 2. However, his other big part in the game is arms dealer Donovan Hock (in Kasumi's loyalty mission) and is, to copy-and-paste from the Heroes entry, "a truly fascinating trainwreck of an accent". It vacillates from American to Irish to Scottish to Russian and back again, often within the space of a single sentence. It was supposed to be a South African accent.
In-universe example: Brooks in the Citadel DLC has an accent that could be described as Australiamericanadienglish, depending on the line. Until she's outed as a bad guy, at which point she turns out to have been legitimately faking it - badly - and returns to an English accent, which she keeps until her disappearance or death.
In Fallout 3, the Enclave President, John Henry Eden, is played by Malcolm McDowell; who attempts to sound like he's from the Southern US, for all of 3 minutes. Arguably justified because he's a supercomputer. Likewise, James, the Lone Wanderer's father, is voiced by the North Irish actor Liam Neeson, and he doesn't hide it too well.
Liam Neeson fits this trope no matter what movie he does.
Canadian VA Gianpaulo Venuta tried and miserably failed to convince players that Far Cry 3 protagonist Jason Brody was a California native. Like the Mark Meer example in Mass Effect, he often slips into Canadian pronunciations, only Venuta does it a lot more often, and not just with "been" and "about."
In Mega Man X4, Iris's voice actress slips horribly during her death scene; she seems to juggle between standard American, British, and Texan, and so turns that scene unintentionally hilarious.note The actress in question, Michelle Gazepis, is Australian.
In Mini Ninjas, most of the voice actors are trying to adhere to a Chop Socky accent, but commonly slip into more genuine Japanese accents. Huh.
Final Fantasy VII has this happen In-Universe when Reeve is identified as being Cait Sith when he begins talking in his natural accent (Kansai in the original, Southern in the English localisation), which he uses to voice Cait Sith, rather than the neutral accent the other Shinra members know him as having. Unfortunately, the game's inconsistent localisation meant Cait Sith loses his accent in many scenes before that, meaning a lot of players didn't realise he was supposed to have an accent...
In Dissidia Final Fantasy we have Gabranth. Played by the Scottish Michael E. Rodgers in Final Fantasy XII, Rodgers did a pretty good upper-class British accent for Gabranth in XII. However for Dissidia he couldn't be reached so Square-Enix brought in The Other Darrin, American-born Keith Ferguson, who voiced Gabranth's brother Basch in XII. Ferguson also doesn't do a bad job of making Gabranth sound British—he just can't seem to decide what kind of British to use, and quite often Gabranth slips from British into outright Cockney. This has inspired the Memetic Mutation "HATRED IS WOT DROIVES ME!" Ferguson toned down the accent a bit for the prequel Dissidia 012. The problem now is occasionally it's too toned down and he slips into Not Even Bothering with the Accent.
Wakka's accent slips briefly (but noticeably) early into Final Fantasy X on the line "A flier? My kind'o customer!"
In Battlefield: Bad Company 2, Southern-Fried Private Haggard is played by a Canadian who puts on a fairly convincing Texan accent. However, there is one anomalous moment in the mission "Crack the Sky" in which he clearly says, "Are you sure aboat that?" in response to a query from Sweetwater.
The original dub of Metal Gear Solid, while an extremely good dub for the time and even today, struggled with this because the actors hadn't quite standardised how the characters were supposed to sound yet.
Revolver Ocelot is a frequent offender. When his arm gets chopped off, his accent changes completely. If you run into the tripwires, he yells "you idiot!" with an accent so removed from either of those two accents that it's difficult to even tell it's the same character. During the torture dialogue where he talks about 20th Century Russia, his accent gains a prominent Russian twang which is usually absent.
Mantis also wobbles between a goofy generically-European twang, and general American. Compare "his mental shielding was very strong" and "the greatest practitioner of psychokinesis and telepathy in the world!".
Sniper Wolf has an accent that is as widely inconsistent as it is unidentifiable.
Gray Fox shifts frequently between a general American and Greg Eagles' own African-American. Possibly cruel to ask someone with a non-rhotic accent to fake a rhotic one while constantly screaming the word "more!". It soon turns to "mo'!".
Liquid's version of Evil Brit Recieved Pronunciation incorporates a lot of American twangs and occasionally turns towards straight-up Cockney.
BioShock arguably does this intentionally to drop hints that Atlas isn't all that he seems.
Also occurs in-universe when a side character from the audio logs is implied to have been killed because she may have caught Atlas using his natural accent.
Likewise, Andrew Ryan affects an American announcer voice in the opening slide show and in other recordings, but sometimes lapses into his native Russian accent when he's speaking directly to the player over the radio. Perhaps the most obvious is when he speaks to Dr. Langford moments before killing her.
Alex Mason, the American protagonist in Call of Duty: Black Ops, is voiced by the very Australian Sam Worthington doing his best attempt at an American accent. He fails completely. Highlights include:
Thankfully, he's gotten a lot better with it by Call of Duty: Black Ops II. The game itself still has some examples, though— Salazar's voice actor sounds as if he can't decide whether the character has a really thick Nicaraguan accent or barely any at all.
In Professor Layton and the Curious Village, Flora's first line, "well, I'd rather not say..." is spoken in a British accent, but she has a Western accent for the rest of the series. Also, from the second game onwards, there are few characters other than Layton, Luke, and Chelmey who even have British accents, despite being entirely set in England!
While Clive, Dimitri, and Claire from the third game have decent accents, the fact that some characters actually sound British makes the fact that some don't really jarring. Apart from Flora, Katia and Don Paolo stand out.
Morrigan's English voice in Marvel vs. Capcom 3 slips back and forth between British, American, and a strange attempt at Irish, even though she's supposed to be Scottish, and her voice actress is Welsh.
Hydrophobia does this to no end, it seems - Kate's accent shifts so often and frequently that it's like an international tour.
In Deus Ex: Human Revolution, Adam sounds very noticeably Brooklyn when trying to talk his way into the DPD morgue. At the time the scene's lines were recorded, Adam's character hadn't been fully fleshed out, so the accent wasn't completely set in stone.
The Penguin in Batman: Arkham City, voiced by Nolan North, is supposed to sound like an archetypal working class London gangster. North's Cock-er-nee accent, worthy of the great Dick Van Dyke himself, varies between "not quite authentic" and "Australian". Perhaps Bob Hoskins wasn't available. May be justified given the Penguin's backstory in the Arkhamverse: he's from Gotham, he just hung out with street toughs while he was supposed to be getting an education in England, meaning the accent sounds fake because it is fake.
Happens again in Arkham Origins, not just with the Penguin, but with his two henchgirls Candy and Tracey. Earlier, when The Joker poses as the captured Black Mask, he tries sounding like the latter, but comes off more like a Mafia gangster (not hiding the fact that Troy Baker voices both the Joker and the fake Black Mask). Then, when the real Black Mask, Roman Sionis (voiced by Brian Bloom), is brought before Batman, the former calls the Joker out, forcing him to scold Sionis for not "play[ing] along" in his true voice!
Shadow the Hedgehog, as voiced by David Humphrey in Sonic Adventure 2 and Sonic Heroes. Shadow would usually speak in an American accent, but a few lines here and there would be spoken in an English accent. This case is strange because David Humphrey himself is American, and Shadow is decidedly not British.
In PN03, during the cutscene when Vanessa discovers the clone of herself, she momentarily loses her German accent.
Depending on the scene, Ulrika of Mana-Khemia 2: Fall of Alchemy can either have a strong Southern accent or no accent. When she's gone for a while without any noticeable accent, the scenes with the southern accent can be rather jarring.
The Street Fighter games have had American, British and other non-Japanese characters since the very first game, which debuted in the 80s, but did not have English VAs until atleast the late 90s. Characters like Guile and Charlie got off with a relatively competent facsimile, while characters like Cammy and M.Bison...not so much.
The commentators in the obscure 1997 sports video game Riot (a.k.a. Professional Underground League of Pain) are voiced by British people trying to do American accents. It shows.
Examples in which this trope is in-character:
During a chat with Mad Moxxi in Borderlands 2, she recounts her past history as a member of the Hodunk bandit clan. She gets so worked up, that she slips out of her seductress voice, and into the same thick, hillbilly accent the rest of the Hodunks speak in (including Scooter and Ellie, her children). She quickly catches herself, resumes her regular way of speaking, and asks you not to tell anyone.
In Borderlands: The Pre-Sequel!, you need to use a secret exit in Moxxi's bar to leave Concordia for the first time. When you open the secret passage, you find Moxxi doing mechanic work in overalls, singing happily to herself in her hillbilly accent. Again, she is extremely embarrassed and asks you not to tell anyone...while the framing device is Athena telling a long story of what's she's done and seen to a group of people interrogating her, who have no reaction to this revelation whatsoever.
A non-regional accent version, but played very straight in Persona 4. Naoto Shirogane, the so-called 'Detective Prince', is a stoic teenage boy who is always serious, polite and correct. Starting from when 'he' meets his Shadow, Naoto's voice has a habit of sliding into its true tone - a softer female register - when angered, embarrassed or otherwise caught off-guard. This is in keeping with her maintaining a masculine façade that forms an integral part of her character - Naoto believes that the police service is a man's world where women don't belong.
Maya Brooks of Mass Effect 3's "Citadel" DLC has a very...dubious American accent, which inexplicably also seems to have more than a bit of Australian in it. This is the first sign that she's not what she seems; after she's revealed to have been Evil All Along, she begins to use her more natural British accent.
Celestia Ludenberg in Danganronpa: Trigger Happy Havoc speaks with a faux-French accent to enforce the image of the graceful gothic lolita gambler. She temporarily drops it whenever she's sufficiently pissed-off, like during her Villainous Breakdown during the 3rd class trial, while she's being exposed as the murderer from an elaborate scheme she came up with. When this happens, she speaks very coarsely, her dialogue absolutely littered with insults and swear words that she would never use otherwise. After she calms down, which usually happens in a split second, she goes back to normal.
Teruteru Hanamura from Super Danganronpa 2 speaks in a rural dialect. When he gets angry, like when people are getting close to outing him as the murderer, he slips into a rural accent that is so difficult to understand that Monomi has to translate for the students. He more naturally uses the accent when he's talking with his mother in a flashback. His English translated version's accent? It's Cajun.
Used in-universe in Final Fantasy VII, when Reeve accidentally outs himself as a spy for AVALANCHE (and Cait Sith reveals that he's Reeve). The former speaks with a Kanto accent in the Japanese version, whereas the latter speaks with a Kansai accent. During the incident with the Mako cannon, Reeve starts speaking in Kansai, and Cait Sith in Kanto. The English version doesn't do this; presumably if they remade the game, they would use American and Scottish accents respectively.
Vanille's voice actress in Final Fantasy XIII is Australian, but Vanille herself can't seem to decide if she's Australian, Cockney (which is the forefather to Australian), or some oddball hybrid of various Australian and British accents. However, it turns out Vanille, and her accent, are from Pulse; something she was trying to keep hidden. When this fact comes out in the open, she stops trying to disguise her accent. Fang, on the other hand, who doesn't have an Australian voice actress, is pitch-perfect Aussie, because she wasn't trying to hide it in the first place.
In Final Fantasy XIV the goblin beastmen talk in Buffy Speak by replacing common words with different ones, such as "tongueflaps" for mouths and "jigglyshinies" for money. There is one goblin that doesn't talk this way and speaks normal English, causing the player character to react in shock since all the goblins they met before had always used buffy speak. This particular goblin explains that he learned how to speak properly in order to reach out to a wider audience for his business. However, he does have a few moments where he briefly slips back into buffy speak when distressed and then apologizes for it while correcting himself.
Zeke in the inFamous series tends to go in and out of his Southern accent with it sometimes being very noticable and other times it will be almost non-existent.
Wheatley in Portal 2 slips out of his British accent in a few places. Listen closely when he uses the extended card-games metaphor and when he boasts about reading books. Since Stephen Merchant, his voice actor, is from Bristol, UK, he was clearly doing it deliberately.
The Spy from Team Fortress 2 has voice clips where he tries to actually imitate the other characters, sometimes to mock them. One that gets used for fan videos quite often is "Why don' we head on beck to tha base, pardner?" in a butchered American Southern accent when disguised as the Engineer. This contrasts to the actual gameplay mechanic of voice commands becoming that of whomever the player is disguised as. It seems the spy himself might not be as good an actor as one would think.
In Grand Theft Auto V, Trevor's mother switches between a regular American accent, a Cockney accent and a Southern accent every sentence. It's probably to highlight how she's just another of Trevor's hallucinations.
In the Ensemble Stars! story Keep In Character!, Akatsuki join the Theatre club to put on Cinderella, despite none of them having any acting skill whatsoever: Kuro tries to play a Prince Charming but can't hold back his rough mannerisms, Keito makes a good effort playing an ugly stepsister (despite being a hilariously inappropriate role for him) but slips back into his normal rude speech when Wataru riles him up too much, and Souma fails so badly even in rehearsals that Wataru gives him permission to just talk like he normally does no matter how strange it sounds for a high-class lady to be talking like an old-school samurai.