I love questions like this, because everyone's got an opinion (much as everyone's got a navel). Let me mention some differences I've noted.
In the US, no one writes "no-one" with the hyphen. Many, if not most, Brits do.
In the US, no one but recent arrivals say or write "whilst." It's correct in British English, I know, but it always jars me.
In the US, very few use the phrase "round the bend" unless they're talking about a winding road on a hillside.
There's a scene in the TV series Frasier where the character Daphne Moon says, "It doesn't matter how often I hear them called an elevator, a truck, or a crossing guard. To me they'll always be a lift, a lorry, and a lollypop man."
American writers and speakers tend toward overstating the case: "It was the greatest thing I've ever seen!" while many Brits understate the case: "It was mildly interesting." (Not a great comparison, but I think the point is the most valid one ever made.)
In the US, a biscuit is bread served at a meal, often filled by the diner with butter and/or preserves. In Britain it's a cookie, which has always puzzled me when watching BBC. (And that's not the only example.)
As shown in dcarson's Carroll quote, many Brits enclose speech in single quote marks and put embedded quotes in double marks. The US is the reverse.
Confusing, no?
A famous wit whose name escapes me at the moment once described the US and Britain as two nations divided by a common tongue. I think he was right.
dcarson, the Dodgson quote was the funniest thing I've read in days. Thanks!
