Welcome to WebmasterWorld Guest from 18.104.22.168
If you're running phpbb look for the one that asks a question in the registration form, this has eliminated all spam registrations on my forum.
There are many reasons for keeping spam out (and removing the spam that's there); you've mentioned one of the key reasons.
Another is that spam lowers the reader value of your forum, and so puts off current and prospective readers.
many forums have loads of lurkers, who will never sign up to an 'untidy' forum.
1. Tighten up security
2. Consider nofollow
3. Moderate more tightly; the quicker you delete spam, the better (in some cases, spammers will give up, though many never even look, they just keep spamming).