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if the same IPs frequentlly appear to you (or may be using whois you got that the authority control the hitting IPs is the same, in case of that scanners using dial-up connections) then call that authority and give them the IP and all possible information (date, time, ...).
Actually, if it's the same IPs repeating the same port scan over and over and over and over and.. well you get the point, it's most likely a worm. Many worms have a "port" scan in them in attempts to find new hosts to infect. I know at my campus there are quite a few machines which recently were infected. IIRC, Blaster is one such worm that does this regularly.