Actually, US spelling was not well received outside of the US until the IT revolution and all the US based software using US spelling pushing everyone in that direction. It then became a case of people being too lazy to correct what the software did.
Ernest, I'm not sure I agree. It wasn't IT that pushed acceptance of American English, but economic strength. British English had a wider breadth, but must less push. However, the biggest influences were the massive American publishing houses and, more importantly, the ubiquitous American movies and television programs. New learners of English tended to pick up what they heard spoken in the media. The acceptance of IT terms was only a follow-up on the earlier trends.
That is an interesting assertion, and one I haven't seen before [regarding Webster's refuted English modifications]. Are you referring to his blue-backed speller, or his later dictionary efforts? I would be grateful if you could point me to a source for that.
Zom, do a simple Wiki search on Webster and you'll see a discussion of both his successes and failures.
As far as the widespread acceptance, it was a slow process. Most people stuck with what they learned in school (i.e. the colonies stuck with British English, while Americans stuck with American English). However, as the American media began taking over the international market (books, magazines, news reports) their word usages get more exposure. The widespread acceptance of popular U.S. movies accelerated the acceptances, but it's still slow. You change language in children, not in people who've used what they were taught as children all their lives.
Ernest, because of my widespread reading in my teens, I unintentionally picked up many British spellings (mostly for longer words). I didn't pick up the more obvious terms (steep, bonnet, etc.), but my writing ended up a composite of British and English spellings. However, I never noticed it until a couple editors started questioning which spelling standards I was using.