As a forum administrator, I spend more and more of my time each day dealing with spammers. I set my membership to admin approval, because I was getting to many spammers registering and leaving spam links! Some prove to be very harmful to an unsuspecting member who checks the link.

To protect my members from the porn, pills and other spam links, I know screen all memberships. Out of 40 or 50 new membership requests daily, I may approve 1 or 2. The situation is really out of hand! I have seen some forums just taken overrun by these spam robots.

I recently found a site called Honey Pot Project, that tracks spammers of all kinds.
Thanks to them I'm finally get a handle on the spam activity and have more time for read Admin duties. Oh did I say it was free? Would leave ya a link, but have not met the posting requirement yet lol!

How do you deal with that problem here?

Lots and lots of work, and the reports of members. :)

It's not as bad here because members can't post links right away (as you have noticed). Also, we have the 90-second timer in between posts. This discourages a lot of the spammers.

Do you require new members to activate their accounts by providing a valid e-mail address? I'd think that'd be the first step to stopping spam.

Account validation via email is step 1
Add a mod that moderates all posts for users with under 3 posts if they post an image or URL
Require members to have 5 or more posts before they can PM
Add a custom question to your signup page, not simply something that requires text but an actual choice or something that can be verified.
Ban a number of the commonly used email domains that spammers use

That'll solve a lot of your issues

What forum software are you using?