Perhaps one of the best known is Vivien Leigh as Scarlett O'Hara and Leslie Howard as Ashley Wilkes in the film Gone with the Wind. When the film came out, it shocked many Americans to see an English actress play a Southern Belle, but now it's hard for us to NOT see them play those roles.
Canadian/New Zealander Anna Paquin doing a Southern accent as Rogue.
In X-Men: First Class, Rose Byrne (Australian) as Moira MacTaggert (where the Scottish scientist of the comics is instead a CIA agent), and Nicolas Hoult (English) as Beast
Days of Future Past has two fictional examples (French Omar Sy as Bishop, Chinese Fan Bingbing as Blink - then again, both characters are children of immigrants) and a real person (Richard Nixon is Canadian Mark Camacho).
Bob Hoskins' portrayal of Eddie Valiant in Who Framed Roger Rabbit. Hoskins' natural accent is a thick Cockney, not unlike Michael Caine's. Here, he does a fairly convincing hard-boiled New York accent, though the film takes place in Los Angeles.
Bob Hoskins plays Mario in Super Mario Bros. with a New York accent. It's one of the few things that worked there.
Cillian Murphy in Red Eye. Wes Craven was initially wary about casting him as Rippner, since Rippner was explicitly written as American. When Murphy walked into the audition, he actually fooled the casting agent with his accent. (The film also has Canadian Rachel McAdams and Scottish Brian Cox as Americans.)
The Dark Knight Rises also has Ben Mendelsohn (Australian) as Stryver and Daggett respectively. Marion Cotillard (French), though the twist makes the Fake Nationality harder to pinpoint.
While with the Grubers, in Die Hard with a Vengeance, when Simon shows up at the blast scene and poses as a city engineer, Jeremy Irons puts on a very fake Texas drawl - which works!
Peter Sellers (English) as President Merkin Muffley in Dr. Strangelove. He affects a sort of flat Midwestern accent that is as "generic" as American accents get, particularly since Muffley was partially based on Illinois Governor and presidential candidate Adlai Stevenson. (He also plays a fake German and an actual Brit in the same film.)
Sellers also played Americans in Lolita (and that character masquerades as a German at one point!) The World of Henry Orient, I Love You, Alice B. Toklas!, Where Does It Hurt?, and Being There. (In the last case, it's an accent whose region can't be identified by the CIA or FBI. Sellers created it by applying an American accent to an imitation of (British) Stan Laurel's voice.) He's one of the more convincing fake Americans when he's "on".
Clive Owen hides his natural Scottish drawl in Sin City.
He hides it but it seems that he can only create a slight American accent if he slows his dialogue to a low, wooden crawl that sounds vaguely British at times.
Many characters of actor Colin Farrell. The most notable was in Phone Booth, in which he slips in and out of his Irish accent, which becomes especially glaring when Kiefer Sutherland mentions "the Bronx in [his] voice."
Also in Phone Booth, you have Australian Radha Mitchell as Colin's American wife; see also Silent Hill, in which she played the main role (and Sean Bean, below, played her husband, both with American accents).
Sean Bean pulls off a very frightening generic American accent as the main character in the 2007 remake of The Hitcher.
Red Leader in Star Wars Episode IV has a quite convincing "mountain twang" pilot accent (à la Chuck Yeager, Tom Wolfe must have smiled); despite being played by Brit Drewe Henley.
Most of the British extras were dubbed over by American actors. Shelagh Fraser redubbed her own voice as Aunt Beru to sound more American, though different takes are heard depending on which sound mix of the film you're listening to.
In The Matrix trilogy, Australian actor Hugo Weaving puts on a slightly exaggerated, sneering Midwestern accent when playing the role of Agent Smith.
And he's almost as bad at it as Rachel Weisz in Confidence. They both swallow their rhotic vowels trying to pronounce the letter 'R,' betraying their original accents.
Though his imitation of Carl Sagan's distinctive vocal patterns and pauses was dead on.
His accent sounds strikingly like Canadian actor Henry Czerny, best known for roles in Mission: Impossible and Clear and Present Danger.
The way Weaving's Rs came out stumbling and drawn-out makes Smith all the more bizarre and creepy. "Good evening, Misterrrr Anderrrrson..."
Word of God is that he was trying to imitate director Larry Wachowski.
More convincingly, from Enter The Matrix and a brief bit in The Matrix Revolutions, is Sparks, the operator of the hovership Logos.
On the other hand, Weaving's voice for Megatron in the new Transformers movies does a good job of disguising his accent under a growling tone of voice that well fits this particular incarnation of the character.
Mel Gibson. While he was born in the US, early in his career you can tell he had to make an effort to cover up the Aussie in his speech. You can definitely hear his American accent slip a couple of times in the first two Lethal Weapon films. These days, when he gives interviews, you would be convinced he never left the US since his birth.
Robert Shaw in General Custer of the West. He does a pretty good job, but his accent falls through a couple times.
Max Carrigan, the incorrigible draftee and brother of the female lead in Across the Universe, was played by British actor Joe Anderson with a sardonic, nasal, and reasonably convincing American accent.
Even more impressive is that he does a great job of singing in the fake American accent.
The Austrian Charles Rooner (born Ernst Robitschek) pretty much made a career out of playing these ones in old Mexican films.
Pretty much the entire cast of Cold Mountain, excluding Renee Zellweger, hailed from anywhere but the American South. Nicole Kidman (Australian), Jude Law, Ray Winstone, Eileen Atkins, and Charlie Hunman (English), Brendan Gleason and Cillian Murphy (Irish), Donald Sutherland (Canadian).
Parodied in Tropic Thunder, which casts an American as an Australian cast as an (African) American. (Originally, the character was supposed to be "truly" Irish, but Robert Downey Jr. found it easier to improvise with an Aussie accent.)
James McAvoy as the "hero" in Wanted. The voice James McAvoy uses normally in his roles (Southish England) is not his real accent anyway (McAvoy is Scottish).
Do double-fakes count? In Blown Away, Tommy Lee Jones (from Texas) plays an Irish terrorist who in one scene fakes a Minnesota accent.
Michael Caine had to play a Texan in Secondhand Lions. And he did a terrible job, too. In promotional interviews Caine said the secret to the Texas drawl is "to let the syllables lean on each other." He also pulled off lousy American Accents in Bullseye! (in one of his two roles in that film) and The Cider House Rules. And he won an Oscar for the latter, yet! Compare to Charlize Theron's far more convincing tones in the same movie (and, in fact, every other film the South African Miss Theron has made – she has yet to play her own nationality on screen).
Christopher Lee did a nice flat Californian accent in the movie Serial – and floating around out there is a recording of him singing Ghost Riders in the Sky with a Southern drawl.
Averted in Shortbus, where the director tried to get Sook-Yin Lee to not sound so Canadian, and finally gave up and wrote into the script an explanation that her character was Chinese-Canadian.
Robert Pattinson does an American accent in Twilight. He discusses it here.
Jude Law's ridiculously bad American accent in I Heart Huckabees. It's painful. He repeats his performance in All The King's Men.
So we're forgiving him for that monstrosity of a southern accent in Midnight In The Garden Of Good And Evil? I think not.
His American accent in an SNLsketch spoofing the classic Twilight Zone episode "Nightmare at 20,000 ft." was also atrocious.
He also did a barely passable American accent in E Xisten Z...however, this is justified seeing as how his American-accented character was just an avatar for a character of his own British nationality.
By that same token, the villain "Red" from Hancock puts on a truly terrible fake... something accent; he seems to have a hard time settling on which one he wants to use.
Before House, Laurie played the father in the film Stuart Little, American accent included. Not to mention his role as Internal Affairs Captain James Biggs in Street Kings (in which his character is remarkably similar to House, sans beard or bad leg).
Dominic West does a pretty good American accent in Chicago (though it isn't a Chicago accent). In Punisher: War Zone however, he attempts a New York Italian accent and the results are not pretty. But it's a Large Ham role anyway.
And let's not forget Catherine Zeta-Jones in the same movie.
In the original cast recording of Mamma Mia! the travel writer's voice is considerably louder and more "Texan" then the other two Disappeared Dad characters. The fact that the musical originated in England probably has something to do with it. Getting back to the film itself, the Irish Pierce Brosnan played an American character, using essentially his real accent.
He did such a fine job playing Major Cabot Forbes in Glory that he probably should have been cast as the lead given that he resembles the real Colonel Robert Gould Shaw a lot more than Matthew Broderick does.
He did a hideous Midwesternish-Southernish accent for Twister though, with just a hint of still being British.
He did a great southern accent in Kissthe Girls as Det. Nick Ruskin but later when he is revealed to be the bad guy and drops the southern accent for a deeper "standard" American one he slips back into his British accent almost immediately.
Incredibly, he managed to play pilot Kent Gregory in Hot Shots in a "blond Californian surfer dude" style (paying tribute to Val Kilmer as "Iceman", of course).
In The Crush, his accent slips to British many times throughout the movie.
In Days Of Thunder, Cary Elwes puts on a decent Southern accent for his role as Russ Wheeler.
He puts on a less-than-impressive Newscaster American accent for The Chase. Luckily for our ears, it was only a cameo.
Ewan McGregor was technically using a Southern accent in Big Fish, but the result was not authentic-sounding at all.
Brian Cox in Super Troopers portrays the Irish-American Captain John O'Hagen, whose accent wobbles between the generic American and Irish depending on his mood, but never sounds Scottish.
While the lead character is played by an American playing a Brit, all the American characters in the newest Sherlock Holmes are played by Canadians. You can really tell with their accents, especially against the British ones.
Emilie de Ravin (best known for playing Claire on LOST) did an excellent job at concealing her accent in Brick; ironically, early on during Lost's run some thought that her natural Australian accent sounded fake.
Sharlto Copley and Liam Neeson are both Fake Americans in the film version of The A-Team. Copley's wanders through several different Southern accents, but given that it's Murdock it fits quite well, and he deliberately fakes a lot of other throughout the movie. Neeson's more or less works as well, though his brogue tends to slip a bit whenever he says anything with an "oo" sound (such as when he tells Face, "You are really tan.")
Isla Fisher, born in Oman to Scottish parents and raised in Australia, only ever seems to play Americans. This is somewhat justified, however, as if she ever did use her real accent, the result would be so cute, the universe would collapse in on itself.
Cate Blanchett in The Gift, with a rather weak Southern accent that results in her being outacted by Katie Holmes.
German movie Locked Up features the main character meeting and falling in love with the "American" Mike while in prison. Mike is just a British guy who has apparently never heard an American speak and wagers no Germans have either. He doesn't even make a flimsy, half-hearted attempt to use anything but his normal speaking voice. Must be a graduate from the Sean Connery School of Accents.
Radha Mitchell (Australian) and Joe Anderson (English) did passable American accents in the Iowa-set The Crazies.
The 1948 film No Orchids for Miss Blandish was made in the UK but is full of fake Americanisms—left-hand drive cars, a vaguely New York setting, and American accents of varying quality. The original novel was written by an Englishman (James Hadley Chase, who wrote a number of novels set in America - although he never lived there) but so thoroughly riddled with Americanisms that English readers mistook it for an American import.
City Island has Emily Mortimer taking part in the exact same twist she did in 30 Rock (that she's "really" an American pretending to be British). Actor Allusion?.
For the handful lines Anthony Head actually speaks in Repo! The Genetic Opera he puts on a fairly convincing American accent. He slips a bit when he sings, though.
The exploitation film American Kickboxer 1 is false advertising on three counts; it wasn't the first of a series, it was filmed in South Africa with the entire cast trying and failing to sound American, and as for the kickboxing...
Aquamarine was set in Florida but filmed in Australia (a change from the novel, where the plot involves one of the main characters moving to Florida - in the movie she's going to Australia), and with the exceptions of Emma Roberts, Sara Paxton, Joanna Levesque, Arielle Kebbel and Jake McDorman, the entire cast affected US accents. Some of them better than others.
Dark City had Brit Rufus Sewell putting on a pretty good accent as well as Australian Melissa George and British-born Canadian Kiefer Sutherland.
Man of Steel has British Henry Cavill was the first non-American actor to play Superman (who, while technically an alien, was raised in America and is considered an American icon). Fans were initially unhappy but most agree he did a very good job with the accent. Lampshaded in the film when he claims "I grew up in Kansas. I'm as American as they come".
Scotsman Alan Cumming had a bit part as an American hotel clerk in Eyes Wide Shut. He tells an awesome story of how director Stanley Kubrick was first annoyed upon discovering on the day they were to shoot his scenes that Cumming was Scottish and not American. Kubrick grumbled: "You were American on the tape!" Cumming coolly responded: "I know. That's because I'm an actor Stanley." Cumming's chutzpah earned the notoriously intimidating director's respect.
Australian Simon Baker in Margin Call, though it's not always ideal (Given that the film has two British characters and it wouldn't be unrealistic for an Australian to be part of the mix as well in a Wall Street investment bank, it's not clear why it was necessary).
British Joe Anderson pulled off a very convincing American Accent in Across the Universe. Amplified by most of his scenes taking place with fellow Brit Jim Sturgess who plays an Englishman.
Most of the main cast of Lawless (set in rural Virginia in the 1930s) are either British (Tom Hardy, Gary Oldman) or Australian (Jason Clarke, Guy Pearce, Mia Wasikowska), and even the Americans in the cast aren't exactly Southerners (Shia LaBeouf and Jessica Chastain are both from California). They all do excellent work, though.
Punisher: War Zone has Irish-born Brit Ray Stevenson as the titular New York native, putting on a pretty convincing accent. The film also has Brits Colin Salmon doing a pretty good job as FBI Agent Butanski and Dominic West with a ludicrously over the top Italian-American gangster accent.
Zero Dark Thirty has Mark Strong (British), John Barrowman (Scottish), Joel Edgerton and Jason Clarke (Australian) as American CIA and Military personnel. All do very good jobs, especially Clarke as Dan.
The President of the United States is British. If you've played Command & Conquer: Red Alert 3, he's particularly eyebrow-raising.
Try the Baroness. Which is pretty damn funny, given the character's origins in the comics.
British Tom Hiddleston does an impeccable American accent as F Scott Fitzgerald in Midnight in Paris.
Small Apartments has Brits Matt Lucas and Juno Temple and Australian Rebel Wilson as Los Angeles natives. They all do very good accents.
Rebecca Hall, like Christian Bale and Kate Winslet, seems to be building her career on this trope as evidenced by her accents in Vicky Christina Barcelona, The Town, Lay The Favorite and Iron Man 3. Her American accent is so effective most viewers would never guess she is actually British.
Iron Man 3 also has the Australian Guy Pearce as Aldrich Killian.
Confederate Army soldier Pencroft is played by the very British Percy Herbert in the film adaptation of Mysterious Island.
The RoboCop remake stars Joel Kinnaman (Swedish of American descent) as Alex Murphy, who is married to Abbie Cornish (Australian). He is turned into RoboCop by the above mentioned Gary Oldman, who works in the same company as Jay Baruchel (Canadian).
Robert Sheehan in Mortal Instruments plays the American Simon and more confusingly, the American-accented boy from north-eastern Europe, Kay von Wollenbarth, in Season of the Witch. The actor is Irish.
English actress Rebecca Hall and Irish actor Cillian Murphy both play American characters in Transcendence.