I have to say, I’m from New Jersey, went to college in Boston, and do a wicked good impression of my friend Bob. 
But I wouldn’t try to pass myself off as a native.
A few oddities I’ve thought of:
Benicio Del Toro’s mumblings in The Usual Suspects which I heard were his way of putting a little meat on the bones of a character whose main function was to be the first one killed. It was a hodgepodge of many different quasi-accents and just plain mumbling.
Brad Pitt’s Spanglish in The Mexican when he was trying to hitch a ride into “towno” in the “trucko.”
Steve Martin asking a French cab driver to “Take me to ze hotel.”
Maybe others will come to me. Maybe not.
Even Keanu did okay accent-wise in that movie. Giovanni Ribisi was also spot-on. Katie Holmes, on the other hand, was dreadful.
There was a British comedy series, 'Allo 'Allo! set in France during World War II. All the actors are speaking English, but with exaggerated accents to indicate what language their characters are really supposed to be speaking; not even understanding what the others are saying if it’s the wrong “language”. Only one that I remember ever translated, switching from a Clouseau-esque French to pip-pip-cheerio-c’mon-chaps English and back again.
And it worked.
Oh, if you want to hear Patrick Stewart do a french accent, rent L.A. Story.
Or hear him gay it up as Sterling, the biggest English queen since Victoria in Jeffrey. “Oooooh… get her!” Wonderful performance.
FWIW I know a few germans and austrians that speak thier english with a fair approximation of an oxford accent, that being what they were taught in school, and what they heard at the time they working on losing thier tutonic accents.
I’ve also been told I speak German with a Bavarian accent…I did have one instructor from Munich, but I thing the main thing is the Bavarians speak slowly, and roll thier r’s mit the tounge rather than in the throat (which I finally gave up on trying to do).
If you’ve seen “Trekkies 2” (documentary about hardcore ST fans around the world…which will make you feel a whole lot less nerdy about your own attachment to ST), a Brit makes the argument that Patrick Stewart is a Yorkshireman, and should have the corresponding accent, instead of the uppercrust, Masterpiece Theater accent that we get from Picard (never mind that he’s supposed to be a Frenchman…)
I came in here to mention this. However, not so much in the context of foreign-accented English. I wonder if anyone else in here thought Harrison Ford’s Russian accent wasn’t all that great: I originally thought he was trying to sound Yugoslavian. Then again maybe I just don’t know accents all that well.
I’m not from around here but I’ve lived here long enough I feel qualified to answer this one:
No, someone from Fall River wouldn’t have a Boston accent, strictly speaking. There is a distinctive Southeast Mass. accent though (which I think is similar to how they speak in Rhode Island).
I have to say I’ve never watched Emeril’s show so I can’t render an opinion on how he talks.
Michael Gambon (who’s Irish IIRC) turned in an uncanny metamoprhosis as LBJ in Path to War (HBO) – the only thing wrong was his accent. He had Johnson’s delivery, growly and rich with layers of character – just not the Texas twang. As close as he could come was a sort of mid-Atlantic muddle.
Fall River
My late uncle was born in Fall River and grew up there and in Brooklyn. He talked kind of like Sheldon “Hey Bud” Leonard, the late character actor. Now was that the Fall River in him or the Brooklyn in him? I wonder…
Boston
As exception to the rule that only Bostonians can do the Bahston accent, I point to Cheers’ Cliff Clavan (Clavin? Claven?). He was played by John Ratzenberger, a native of Bridgeport, CT.
Colin Farrell as Alexander the Great sure sounded a heck of a lot like Alexander the Irish Guy Who Couldn’t Quite Lose the Brogue.
Well foreigners attempting Irish accents for movies is always worth a few laughs. Several of the worst are probably Tom Cruise and Nicole Kidman in Far and Away and the Bridge brothers in Blown Away.
Although its much mocked Brad Pitts northern Irish accent in The Devils Own was pretty good, although he spoke a little too slowly and you could tell that he was thinking about what he was saying it was more than passable.
How was his attempt at an American accent in Tigerland? It sounded decent to me but I’m not from there.
What accent is Triumph the Insult Comic Dog supposed to have? Hungarian?
Don’t be too surprised if, during your research into the actual Brothers Grimm, that they also didn’t come across any walking trees like in the movie too.
Having seen the Japanese-dubbed version of Breakfast at Tiffany’s on TV a while back, I can say that Mr. Yuniyoshi was dubbed with a very over-the-top voice performance, almost as hammy and stereotypical as Rooney’s original.
But they did cut out half of his screentime. 
It has been awhile since I’ve watched Tigerland so take my opinion with a grain of salt. If I can remember correctly, his character was Texan, and as a native Texan, I would say his accent was pretty good, better than many fake Texan accents I’ve heard, but still obviously fake. And I could tell some Irish coming through at times, like when he was yelling.
Jeff Bridges…I really like him, but his accent in Blown Away was, well, blowing all over the place, from Boston to New York to California.
I must agree that 99% of all fake Southern accents are awful, but one in particular is so bad that it deserves singling out: Nicolas Cage’s Alabama accent in Con Air. I’ve lived in Alabama for 20 years (and have lived in the South all my life), and am only about 1 1/2 hours drive from Mobile, where his character hailed from. I have YET to hear anyone here speak with the accent he used.
I also have to say that I remember being incredibly impressed with John Hillerman’s Texas accent in some episodes of Magnum, PI. I lived in Texas around that time and that was the first time I remembered hearing such an accurate-sounding portrayal. I felt really stupid years later when I found out that he is a native-born Texan and that the English accent was the fake one!