If you're not an american citizen your options are unlimited.
With regards to the yacht, if you're docked at a port, your presence in the country will be recorded.
Most countries will allow you to stay for 3 to 6 months on a tourist visa. After you're present in the country for more than 180 days out of a year, you're likely to be considered a temporary resident of that country and would most likely to subject to the tax laws and obligations of that country (On any income earned while there - whether the money is earned within the country or not)
Countries have double taxation treaties that exist to ensure everyone pays at some point. If you're a citizen of one country and a resident of another, you will in most cases have to pay taxes in the country you are resident in.
Think of it like this - if you're using their system they will expect you to abide by the tax laws.
If you really wanted to live on the yacht and avoid taxes, you would need to spread your time between a minimum of three countries per year, for less than 180 days each. This includes your country of citizenship.
However, you do not need a yacht to do it. You can do it without a yacht as well. This is one reason why Formula 1 drivers and Pro Tennis Players drivers never pay taxes. They are never in any country long enough to be deemed a resident.
While you are not present in your country of citizenship, you will need to provide a letter to the tax office stating that your were not resident during the tax year and did not earn any income in the country.
If you going to do the above, it's probably best to have an offshore entity to manage your assets though.
And that's about it.
Runningbear