It's also a well-known and popular fact that I'm a shameless anglophile, born and bred in Virginia but raised on ancient PBS reruns of the BBC — to the point where I have a British sense of humor and a tendency to drop phrases like "it's a fair cop" into everyday speech and then wonder why people are looking at me so strangely. I have in fact had people inquire if I was originally from Britain, presumably because I give off a general vibe of not being from 'round 'ere — although I can't imagine anyone really familiar with dialects asking that.
Thus, I found this item on the BBC news website to be interesting — it's a voice coach who teaches Yanks to talk like Brits, and Brits to talk like Yanks. :) Usually hearing Brits "doing American" ranges from "painful" to "hilarious," as they sound like they're pinching their noses and talking like Edward G. Robinson. Even Hugh Laurie (who overall does a very good American accent) occasionally succumbs to this, although Bob Hoskins manages to avoid it.
Since I've become more aware of such things, I've noticed however that I do sometimes unconsciously slide into a Beeb sort of accent, especially if I'm actually around anyone from the UK. Not "putting it on," it just comes out that way. When I realize I'm doing it, I usually get very self-conscious and wonder if I'm coming off as pretentious.
On the other hand, if I could choose any one voice in the world to have, it would be John Huston. :)