How To Make Freeloaders Not Spam AGAIN

Let us suppose you run a free service, that gives out web page space or email accounts or whatever, to any random luser who wanders in. Therefore, you can't demand a credit card number up front, so your chances of collecting on a fine are somewhere between "slim as a monomolecular fiber" and none.

One of your lusers decides to spamvertise his page, dropbox, or whatever, that's on your server. (If he's spamming from your server, you have been inexcusably irresponsible in your setup!) You shut him down. But... the next minute, he's right back, setting up another account, spamming... and ruining your reputation. What to do, what to do....

Some options: