Blocking Destructive Users from Websites?

billmarrs asks: "I occasionally need to block a user from using my website because they are abusing the system in some way, but the tools I have to work with for blocking them are easily circumvented. Once I identify them, I can block their IP; but they can just hang-up their modem and dial-in again to get a new IP. I can also stick cookies in their browser to identify them, but they can delete the cookies (or turn them off altogether). Are there other ways to block unwanted users from one's website?"