I agree with Harregarre on the spelling of words, although I'm not quite sure which one of "realise" and "realize" is British English and which one is not. Gotta check that over.
As of the pronunciation, the most important difference is the pronunciation of "r", while Americans pronounce the letter explicitly, British people pronounce it more like "w". So "promised" might sound like "pwomised". Also, when a word ends in "r", British people do not roll their tongues. As a result, "car" may sound like "cah" (with "h" silent), and "redder" may sound like "redduh". Other instances of pronunciation include:
either - ither (British); ether (American) - with the first letter pronounced as its original sound
often - ofen (British); often (American) - letter "t" pronounced explicitly in American English
etc. (ok, I admit I can't think of that many examples in a moment)
Also, I don't know if many have realized, but my feelings are that American English is a little more "conversational" or familiar than its British counterpart. The difference somewhat shows in certain structures of sentences, which I still have to think over. I think that's culturally related - British English has its sediments through centuries of development, while American English developed rapidly in the recent two hundred years. However, I'k like to point out that I didn't mean by the obove that any one is supposed to be better than the other.