I have been asked the following in the USA.

1. By a chap on a plane who told me the USA is very grateful to Tony Blair for the support he gave Bush in GW2. "Please could you thank him personally when you get home" he asked me. "OK, no problem, I'm seeing him next week" said I solemnly

2. On many occasions on saying I'm from England I've been asked, "Oh I have a cousin / aunt / distant relative in (any city). Do you know them?

3. What is the difference between the UK / England / Great Britain

4. Why do all English actresses have bad teeth? . That one really confused me although someone has since mentioned it was something Jay Leno talks about?

5. Do you Brits have lots of car crashes seeing as you drive on the wrong side of the road?

6. (This one has nothing to do with the USA - both were Scandinavians IIRC). I did a season on a cruise ship years ago and my two favourites were:
a) Is there a pool table on board? (20 years on this one is still the funniest)
b) What time does the midnight buffet start?

However, I confess to standing in The Mall in downtown DC last year and trying to orientate a map vs which direction I was facing. "Excuse me, but where is the White House" I asked a passing couple. "It's that huge white building you are staring at" came the response.