[theantidote]

As a student I say "Yes!"

Just require a valid .edu address at sign up and send a confirmation email. Allow students to put in their edu email as well as their personal email because I really only use my personal account, as do most of my friends. Just send a confirmation email each semester or something as recommended by another commenter and that should be strong enough verification. Some people may try to cheat the system by either using an alumni email address (which you should filter: alumni.*.edu) or purchasing an edu domain to host their own email on, but those are both very unlikely and I doubt you'll run into them often if at all. There is at least one school that I know of that doesn't give out email addresses to its students anymore (Boston College or University, I forget which one); for those students just put a note next to the .edu field saying something along the lines of "Your school doesn't give you .edu addresses? Just email us and we'll help you out."

I don't think there's much else you can do to verify student accounts. If you're really ambitious you can ask for the student's ID number, full legal name, and university and then call up the registrar office to verify their registration. My school also participates in the National Student Clearinghouse: http://www.studentclearinghouse.org/ but it costs money for each verification. Obviously these options are kind of extreme and I'm pretty sure only banks and hiring agencies would spend the time verifying an enrollment this way.