I think it's important to add that if you are an American living abroad you still have to pay taxes to the United States even though it is lower
If you are from most other nations I know at least for the UK if you don't reside in the United Kingdom you don't pay taxes
For the USA the only way to be free from the American taxman is to renowns you're American citizenship
The only way to do with that is to go to an embassy and request to give up your citizenship
If you do that you'll need a global citizens passport or a passport from another country