And no, the dollars are not eligible for Roth IRA contributions. Sen. Warren tried to fix this earlier in the year (unsuccessfully, so far)
Also, some states treat graduate stipends specially. In Pennsylvania, the stipend is exempt from state and local income tax.
I'm new to the U.S. tax system. What do you mean by that? Isn't tax mandatory? I mean, either way you're going to have to pay up, be it every month or when tax filing time comes around.
I'm actually applying for the GRFP this year, but I'm not sure how my university handles the funds.
Stipends are generally considered "awards" and not "wages", so Social Security and Medicare taxes are not withheld. There's no free lunch, of course, because each quarter that those taxes are not withheld are quarters that don't accrue the "credits" needed to qualify for Social Security benefits. This could be an issue for someone who, for example, became permanently disabled at a young age. Most people, of course, will work enough years after graduate school that they will qualify for Social Security benefits, but it is something to consider.
I think it's standard at this point for universities to not withhold any tax from stipends (or the stipend portion of a disbursement to a graduate student if they are paid from multiple sources). Of course, income is income, whether it's "earned income" or not: so it's not like there isn't a tax liability just because the university doesn't withhold tax.
Note that all this is even more complicated for foreign nationals, for whom some combination of state and federal taxes may actually be withheld depending on the specific tax treaty that applies, the visa status of the student and current IRS policy.
Also, unlike Medicare, Social Security qualification isn't binary, your actual benefits are based on your wage-index-adjusted lifetime SS-taxed earnings, so even if you qualify, the period of not contributing means lower benefits. (Now, if you've also had enough contributions to max out your benefit level, that doesn't matter, but that's a smaller share of people than those that will merely qualify for SS through post-graduation work.)
The government doesn't really know about when you were paid though, so you're unlikely to get hit with penalties if you do forget to pay the estimated tax.
It makes it really fun when you and your spouse are both grad students, and have to deal with that twice.
[1] Okay, not everything, but for the purposes of this discussion, yes.
There is more to "tax status" than whether you must pay income tax. There are payroll taxes, Roth IRA-eligibility, etc.
For more, read Pub 970. It's really quite complicated than whether you pay taxes on the income or not.
Not all graduate stipend (fellowship, etc.) income is taxable, but the part that comes from work (as well as any amount not used for certain purposes, even if it doesn't come from work) done as a condition of the stipend (fellowship, etc.) is taxable:
Suing them is not a good idea, but why not report them? It's not like retribution will come your way and it could be interesting, if not better (as in "less contradictory") for future people in your position.
And funds that come through my university do get a W-2 come tax time.
I received a NDSEG as well and my research showed up a lack of homogeneity in how each school handles things.