After expatriation, you will be treated as any other country citizen is treated. Suppose you are a citizen of a visa-waiver country. In that case, you won't need a visa for visits up to 90 days to the U.S. If your country is not on the visa-waiver list, you will need to apply for a visa, but, barring any unusual circumstances, you will most likely be approved. Refer to our discussion of legal rights after expatriation.
Regarding U.S. taxes, you will be treated as any other citizen of your country in almost all respects. Assuming you live outside the U.S. and don't have a green card, you will be taxed as a nonresident on any earnings from U.S. sources. This will allow you to avoid paying U.S. taxes on interest and capital gains.
How to meet the substantial physical presence test
You will, however, be taxed as a resident if you spend enough time in the U.S. (including U.S. territorial waters) to meet the criteria of the substantial physical presence test. In other words, if you spend:
At least 31 days of the current year in the U.S., and
At least 183 days over 3 years including the current year and the previous 2 years were spent in the U.S. This is calculated by counting all of the days you spent in the U.S. for the current year, 1/3 of the days you spent in the U.S. in the previous year, and 1/6 of the days you spent in the U.S. the year before that.
Essentially, according to the terms of the substantial physical presence test, you can spend an average of up to 4 months each year in the U.S. and not be considered a resident for tax purposes.
Note: because of the different weights used to count days in each year, several permutations of time spent in the U.S. are possible. For example, you could spend 180 days in year 1, 120 days in year 2, and 110 days in year three and still not be considered a resident for tax purposes for any of those years.