Script kiddies in general are annoying flies that deserve to be swatted. Anyone who runs a system connected to the internet with halfway decent logging will see them regularly knocking on the door with the exploit of the month.

Script kiddies tend to use scanners to scan large netblocks for potentially vulnerable hosts and canned exploits to attempt exploitation. Unless you've pissed them off in IRC or have a web page they're intent on vandalizing, they probably won't stay around long if the first exploit dosen't work - you won't generally see concentrated attacks. The large number of insecure hosts on the net makes this bulk scanning worthwhile and provides them with hosts to act from. Bulk scanning also increases the likelihood that someone will notice, complain, and get the box taken offline. In order to counter this, kiddies may select a throwaway machine to do the scanning from and, if they're using a blind exploit, another machine to come back and check to see who's been compromised.

What they want the machines for is anyone's guess, but it's a good bet that they're interested in defacements, warez, or IRC wars.

The most common activity I see are automated scans for systems offering anonymous FTP. I assume that they're interested in it either because they want a warez base or because certain ftp exploits require writable directories. I see between one and four probes a week on my systems, although those on a /24 in an academic network seem to draw more attention than those on a pair of /28s on a commercial ISP's DSL lines.