No, this is not a case where they don’t even bother; like Sean Connery or Jean Claude Van Damme. This is those, whose actual accents keeps slipping through, noticeably in every work.
Andie McDowell; she does not use a Southern Accent usually, but it keeps breaking through all the time; sounds like the character is doing a Scarlett O’Hara impression.
Aiden Gillen on Game of Thrones; ca’;t seem to decide from one sentence to the othe whether he is going for Irish or RP.
Costner pretty much sets the bar.
One obvious answer is Charlie “Jax Teller” Hunnam. He’s a good actor when he’s using his native accent but he did not quite cut it as a biker from California.
His accent is a perfect blend of The Fingers where he was born and the Riverrun accent of where he was squired. Prove that I’m wrong.
Colm Meaney’s American accent is pretty bad.
Halle Berry.
I’ve never heard him do an accent.
If you mean the pseudo southern accent she used in Monster’s Ball, then I couldn’t agree more. It was a gripping film and she did okay with the part but I think she would have merited that award much more if she’d worked with a dialect coach.
Hayley Atwell, yes, I know she was born in London, but both her British and American accents sound forced and fake. 
Dont get me wrong, they arent Costner-level by any means, and i like her as a actress, but both accents are just a bit off to me.
I thought she meant the pseudo African accent she used in X-Men and forgot about halfway through the movie.
Yeah, I guess he doesn’t fit the OP, since he did Robin Hood without even attempting (at least, in final shooting) any kind of accent. I believe there are hilariously bad outtakes of early attempts.
Christopher Lambert’s… extremely peculiar accent has to fit in here somewhere. Not sure where.
Carrie Fisher’s sort of bizarre attempt at a British accent in some scenes of Star Wars have to qualify, too. Has she done accents in anything else?
Did you see Jimmy Fallon trying to do a Jersey accent on SNL? 
Everyone in NCIS: New Orleans. Well, almost everyone as CCH Pounder is not bad but the rest give me a headache.
Thirteen Days - Nuff said.
As for mine: Gary Sinise in Truman.
I have lived less than 20 miles from the Kansas City, Missouri area for my entire life. I have never heard anyone here sound like that.
In the SNL skit last Saturday with him attempting a Philadelphia accent, the others were openly mocking him.
Well; (A touch NSFW).
Sure and that’s exactly how everyone I know who was born in The Fingers and grew up in Riverrun sounds.
Juiia Roberts in Michael Collins.
David Boreanaz in *Angel *had a worse Irish accent. But he wasn’t a major movie star in a serious big budget film. And he only used it in flashbacks…
Dick Van Dyke in Mary Poppins.
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