FYI:
No matter what, you owe Federal Tax on any money you receive that does not go towards tuition, fees, and required stuff for your courses. Therefore your living stipend is taxable.
source:
http://www.irs.gov/individuals/students/article/0,,id=96674,00.html
(see "Taxable Scholarships and Fellowships")
However, the question is in what situations do you get taxes garnished on your stipend. The federal government makes a subtle difference between receiving a fellowship for training and getting paid wages in return for work. Essentially, the IRS thinks that a training fellowship (F31/F32, DOD, etc. or if you're fully funded on a slot on the main MSTP training grant) is a gift, while if you're paid from your mentors
R01 or similar grant you are considered as personnel paid wages working to complete that grant.
If you get a portion or all of your stipend paid from an R01, you will get your taxes withheld, and you will receive a W-2. If you have a F31 or you're in your medical school years, you are not "working for pay", and you don't receive a W-2, and you don't get your taxes garnished.
A few notes:
1) Even if you don't have a W-2, you still owe taxes! And since you don't get taxes withheld, you have to pay-as-you-go - otherwise you will pay a penalty to the IRS.
2) If you have you taxes withheld, there is an advantage - working for pay is defined as "earned income" which means you can qualify for a Roth IRA, for which the tax sheltered benefits and compounded appreciation between now and your retirement probably far exceed the small amount of taxes you pay now.
3) Depending on your jurisdiction, state and local payroll taxes may or may not be withheld depending on the source of your stipend. Check with your payroll and accounting department for more information.