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!
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.
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.
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.
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.
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.
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.
Wakka's accent slips briefly (but noticeably) early into Final Fantasy X on the line "A flier? My kind'o customer!"
Revolver Ocelot's accent changes completely when Gray Fox lops off his hand in Metal Gear Solid.
Happens in-universe when we slowly get the indication that Master Miller isn't Master Miller.
In Peace Walker, Strangelove can pull this off around twice a sentence.
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.
Despite maintaining a decent American accent for the most part of Call of Duty: Black Ops, Sam Worthington's Australian accent really does come through at times - Most notably, any time that he tries to shout or act emotionally.
Thankfully, he's gotten a lot better with it by Call of Duty: Black Ops 2. 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.
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.
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.
During a chat with Mad Moxie 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 a thick, hillbilly accent. She quickly catches herself, and resumes her regular way of speaking.
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 fašade 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 Trigger Happy Havoc: Danganronpa speaks with a rather 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 her real name, Taeko Yasuhiro, is revealed and she admits defeat, she drops it permanently.
Similarly, Teruteru Hanamura from Super Danganronpa 2 speaks in a rural dialect. When he gets angry, like with Celestia, 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 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.
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.