What you're probably seeing is port scanners. They scan IP's that are connected to broadband ISP's trying to find openings for whatever purposes (kids goofing off, enemy agents trying to find industrial or military secrets, ehatever). My router sends me a log full of them every 4 hours or so. I've given up trying to trace them, WHOIS, email the ISPs,or whatever, only to hear "Thanks, we'll look into it"... I just ignore them now. Make sure your router/firewall is set to stealth (go to Gibson Research Center
and look for the "Shields Up" tests.