At United States PhD programs, is the research / TA stipend taxed as income tax? Is the research / TA stipend for PhD students at U.S. universities taxed as income?
This is really a question you should pose to an accountant since there are a fair number of conditions here that affect whether you owe any taxes.

Stipends are, generally, not considered wages, in which case you wouldn't pay Social Security or Medicare taxes.

However, they are usually considered taxable income, so you would need to pay federal income tax.

Then there are state taxes to consider; with 50 states plus DC and other territories, that's too broad a question to sensibly answer here. 

In some areas (such as NYC), there are local taxes to consider as well.

However, if your stipend qualifies as a scholarship because it is "...granted to meet the cost of education", then it may be tax-exempt.

This IRS Topic 421 is a good starting place, but US taxes are complicated and expensive if you get them wrong, so I strongly recommend getting professional input here.

ALSO US citizens have to file taxes every year, regardless of where they live. Whether they have to pay taxes depends on tax treaties and local tax laws.

This might also be true of your country of citizenship. Again, the only way to know for sure is to talk to an accountant.