Some actors find it hard to turn accents on and off, and decide it’s easier to stay “in character” and retain the accent they’re using for as long as they’re working.
When English actor David Suchet was playing Hercule Poirot, he kept speaking in a Belgian accent offstage, because it would take him forever to get the accent right again if he dropped it.
He seems to have known that made him seem like a Stanislavsky fanatic, but hey! He did a great job, so whatever worked for him is fine by me.
In the Simpsons episode where Apu was going to be deported and bought a fake identity, Hank Azaria put on a terrible American accent. “The Nye Mets are my favorite baseball squadron.”
Tatiana Maslany on Orphan Black her character are all clones and sometimes only distinguishable by their accents… and (inevitably) they are always switching roles and “faking” each other’s accents.
This is kind of stretching it because I have no idea whether or not Tina Fey grew up with a Philadelphia accent (she’s from a Philadelphia suburb, Upper Darby) but a couple years ago she did a sketch on SNL in which she turned on a Philly accent.
This is one that didn’t happen, but I really wish it could have.
Leonard Nimoy grew up in Boston’s West End (which was bulldozed in the 1960s and replaced by condos, a highly controversial action that destroyed a traditional neighborhood) with , by his own admission, an atrocious Boston accent. He struggled to get rid of it for years, taking voice lessons and eventually stuttering before becoming the rich-voiced thespian we know. He’s done many accents and roles over the years, but to my knowledge has never done a Boston accent. (When he voiced an opening for the Omni Mugar Theater at the Boston Museum of Science – “I grew up three blocks from here” – he didn’t “put on” an accnt, although that would’ve been the perfect time for ir).
Anthony LaPaglia is Australian, but has spent much of his career playing mobsters and tough cops with Noo Yawk accents.
One of the only times he’s ever used his “real” voice was on “Frasier,” where he played Daphne’s brother. Apparently, American casting agents couldn’t tell an Aussie accent from an English Mancunian accent.
In an episode of BTVS, Spike, a british vampire played by american James Marsters is hiding out in the ruins of the High School. When discovered by soldiers he puts on the most awful American accent to say “I’m uh frend of Xanderz” when asked who he is.
The guy playing her gay bestie/brother is also not british but canadian. I dunno if there were instances of using that accent for the character or not.