I've talked at length about the reasons why all schools -- but especially colleges and universities -- should have a clearly written and well published "computer users' rights and responsibilities" document to go along with the institution's code of student conduct. In fact, before any student is granted an account on your university network they should be required to acknowledge and accept this document and agree to abide by it.
Most of you will say that that won't stop them from using your network to steal music and videos -- no matter what countermeasures you have in place. Well, maybe not. But, if your institution is committing a full-time employee to fielding complaints from the RIAA, maybe it's time to try something else.
Even if your institution is not being threatened by the RIAA, the costs of simply dealing with requests from the RIAA can be staggering and it's time to hold your students accountable. If threats won't do, then hit them were it hurts. Put a fine on their Bursar bills for each instance of theft reported to you. Then let them explain to their parents(most of whom are footing the bill) that the fine is for stealing music and that the next time they are caught, they could lose their computing privileges to boot. Then make them pass an online test regarding copyright infringement and it's implications.
Like it or not, copyright infringement is stealing and it hurts nobody but the artists themselves who signed their rights away in exchange for royalties paid for each copy sold (not stolen). And, like it or not, nobody can seem to touch Kazaa and their ilk so it is left to mothers of bright (but undisciplined) children and the universities they attend (one of the few places sure to have a suitably robust network) to reign these kids in.