Liam Neeson does a credible job on several American accents.   I also was amazed when I found that Bob Hoskins was from England.

Some actors just seem to have a lot better ability and voice to cover a wide range with some good coaching. Others are simply trapped with a certain voice which will always be there no matter what they do...and some of them don't try too hard! Costner is an obvious example. I don't know how hard he tries at the accent, but it always has his somewhat strange (as PT pointed out) voice beneath it which just makes it all the worse!

And doncha' just really enjoy those movies where the "big star" is completely crap so he ends up with no accent surrounded by actors who do? Ever see "The Blue Max?" Every German in the film is speaking English with some kind (often quite good, some bad) German accent. George Peppard, the "big star" is also portraying a German, but seems to have lost any and all vestiges of German in his voice.

Spaw