Tor can be used for good and for bad. It's the very same problem that Cory Doctorow talks about in his lectures about the War on General Purpose Computing, and it's not an easy problem to solve. I'm an admin on a social/gaming site (a MUD with appendant forum, blogs, and other community elements), and we have had to make a few decisions about Tor in the last couple of years. Some background: the site is quite old, an…
Assuming you have the technical capability, requiring an email address and confirmation for only tor users could work. Freenode does something similar - tor and other problematic traffic sources can connect but must use connect time SASL to authenticate to a previously created account, which is sufficient to exclude the vast majority of the griefers.
Having said that, I'm currently trying to make a point of using TOR for regular and mundane uses - particularly if using government sites - just to increase the amount of "legitimate" tor traffic. I'm also (carefully) intentionally de-anonymising myself while using tor like this - identifying myself to local government websites while doing "ordinary" things while connected over TOR - I booked an extra trash collection recently for example. I don't suppose my local council website managers even notice, but I like to think my local PRISM equivalent operators see traffic like this and think "WTF?" ;-)
(But like the parent-poster, I've suffered forum-trolls, and given the time and skill poor nature of most forum owners, the obvious "just ban free email accounts/tor/cellular-ip signups" is often the right, if overly broad hammer.)