honey pots

How do unprotected PCs get infected by viruses "mere seconds" after being connected to the internet? Are there computers just shooting around the internet looking for open ports? Isn't this flood somewhat obvious (and shouldn't identification of the source allow at least the zombie computer to be disconnected)? And, finally, when my firewall is down for a second (switching, as it often seems to, between Norton and Windows firewall), is my machine getting zapped?