There is a free report from International Living that provides details on the tax implications of living in various countries as an American citizen.
So, does living abroad mean a tax savings to the American expatriate? Not necessarily. There are some countries with low tax rates which may mean savings, such as Panama. There are other countries that have double-taxation treaties with the USA, including France and Mexico.
For a detailed answer to the question, there's a book you can order, The Expatriate's Tax Bible. Or, you can check with a tax professional who works with expatriates - either in the US, or in the foreign country you're investigating. Search Google for "expatriate accountant" and you'll find a list of pros to answer your questions.