This is a great question and one I'd love input on as well! 

We've used them for a variety of things depending on what our needs were for the summer. We had to get some basic stuff done that no one else had dedicated the time to do like completing employment verification's, uploading Moving and Relo data to the master tracking sheet, I taught one of them how to do sourcing, etc. One summer we had one working with the recruiting team on basic functions and the next summer we had them working with the benefits team. You can let them do a lot-assuming you are paying them. Explain to them the sensitivity of the work/data in HR and you should be good to go.  

I worked out a program with the University of Tennessee to hire seniors for a semester with the option to continue them for an extra semester. They would get course credit, we'd get much needed help (10-20 hours weekly) and they got experience for their resumes` and job hunting. Depending on their skill set, I'd let them do everything from recruiting, orientation, data input, offer letters, submitting drug and background checks, processing benefits, etc. Nothing was off the table. That said, we determined that it would be better to work interns on "projects" like update the handbook, re-write job descriptions, send out surveys, and/or update policies. At the end of the semester, I'd complete an assessment, send it to UT for their professor to review (part of grade), and then attend an employer appeciation breakfast. I found the interns to be very productive and the relationship with the University a Win-Win situation.