First off: I'm from England.
There are some interesting points raised here. I haven't read every single reply since the thread started in 2003, but here's my thoughts:
1 - the number of different accents is not limited to the number of countries that speak English (US, UK, South Africa, Australia etc), but each region or even city has its own accent. A native speaker can usually tell to within 50 miles where a speaker comes from, and to what social class they belong (in Britain at least).
2 - there isn't a right or wrong about accents, you just pick up what you are exposed to.
3 - it is difficult to try to emulate an accent convincingly, you just pick up what you are exposed to. It is difficult to fool a native in this respect.
4 - people from different countries often have similar idiosyncrasies, regardless of how they try to modify their accent. Many japanese, for example, have a similar sound (to British ears) when they speak English. Ditto Indians. Ditto other European nationals. However, those who were born here (regardless of racial background) may often have a perfect accent that relates to where they were brought up.
5 - Many English people find the American accent "cool", but some dislike it. Some think that speaking like an Australian makes them sound "laid back". Many feel that Irish brogue makes people sound charming and confident. These are stereotypical attributes. It is difficult to say what a British accent is, from my perspective, because there are so many. "BBC English", also called "received pronunciation" is generally felt to sound "stuck up" and upper class. It is also to some extent artificial. However, it is designed to be clear, so it is not without merit.
6 - I heard a Black American say that when he was in England, people noticed first that he was American, and noticed only secondly that he was black. This meant that he was not treated with the prejudice that many British black people encounter in their own country. They were more interested in what he was doing here and what life was like in America! The power of accents is indeed powerful!
7 - When I was in the US, the first thing almost everybody said was "Gee, I love your accent!". The second thing was either "Do you know so-and-so?" or "Are you Australian?" (As if British sounds like Australian!)
8 - The American accent receives a lot of (presumably positive) exposure due to Hollywood. So British people are never surprised to hear "foreigners" speaking English with an American accent.
In the end, I think you just end up with whatever accent you hear around you the most. My own accent changed when I moved from the countryside to somewhere near London as a child. Some people never lose their accents, others adapt quickly to new surroundings. It doesn't really matter, as long as you can be understood. Like I said earlier, some accents are associated with different traits (relaxedness, stupidity etc), but there isn't much you can really do about it anyway!