Q: Is it legal to have an unpaid student intern for my professional services business?

A:  In Massachusetts, you can not have unpaid internships UNLESS an exception applies. One awesome exception is for student interns providing professional services (like writing code).  However, you still have to be careful as there are Department of Labor and Massachusetts Division of Occupational Safety rules to determine if the relationship look more like employment.  If you are not a charitable organization, you can not rely on the DOL's "volunteer" exceptions as your professional service organization does not lend itself to a noble cause without a big stretch of the imagination.

Unpaid student interns should be operating in an academic environment ripe with training so if your intern is performing tasks ordinarily done by paid workers and without special training than in most cases they should be treated as employees (min wage, payroll taxes, etc).  

They can work on things that you need but you should make sure they are getting a good deal too.  

Unpaid student interns should not displace employees or interfere with the employment opportunity for others. 

Unpaid interns should be there primarily for their own benefit.

The relationships should not last longer than 3 months.  

So, If you get lucky and get a graduate science student who is willing to do unpaid work and you don't want to get sued, give them the glamour that they are looking for on their resume and allow them to do what they expected to do (e.g. write code for you) and not extensive admin duties like making coffee.  

It would be wise move to draft and sign an agreement that makes clear the fact that they will not be paid wages, the duties and responsibilities, what will be paid under certain conditions, and the general understanding of both parties very clear.