1) Add nofollow to all links, so that spamming links is pointless for SEO (spammers are usually too stupid to understand this, but it makes their work redundant at least)
2) Stop people posting links in signatures entirely
3) When signing up, have a spam-detector question relating to the subject of the forum (eg if it's about Doctor Who, have a pic of a Dalek and ask "What is this?")
Even then, you might be the target of spam. I've seen a very sad spreadsheet used by "SEO companies" (read: spamming pieces of crap) with a list of forums, including this one, and details of how to spam it (eg "Register, wait a day, post something in Off Topic, wait a week, add link")
If an SEO company has put your forum on its spreadsheet, you're kinda doomed for now, as 10,000 people in Asia will be "working" for the SEO company, signing up for 50 Yahoo Mail accounts each to create usernames and post links.
I've uncovered a lot of SEO companies that just employ people in Asia to spam links on sites. If anyone reading this works for an SEO company, go die in a fire. You do nothing to make this world better.