How Do You Handle Portscanning Attacks?

Kainaw asks: "I tried to submit this earlier, but I couldn't because I had no bandwidth available. The reason is simple: I use Comcast for cable Internet. My modem/router is portscanned constantly. Nothing makes it past the router, so everyone tells me that it isn't an issue. Well, it is when I can't access any webpages, get email, or even submit a simple article to Ask Slashdot because my entire bandwidth is eaten up by script kiddies with a new portscanner toy. This is a two-part question: First, can anything be done with a simple at-home modem/Linksys router/two computer setup to stop a portscanning attack? Second, is it possible for the Linksys router to become a 'bot' and actually be the originator of much of the traffic?"