Tax laws change all the time, and even when they don't, there are exceptions. But let's get a flavour of the problems. Firstly comes the passport. In most countries, the passport is actually irrelevant for tax purposes. That US passport, or green card for that matter, makes you a good customer of the IRS wherever you go.
Residence is the main consideration in most countries for income tax purposes.
Residence, that is, in a tax year. And the definition of residence varies slightly from country to country. The notion of domicile often comes up in common law countries. Then comes the location of assets. The beauty is that many such problem areas can be avoided with proper planning.