There is no such thing as a secure internet-connected computer. Operate on the assumption that anyone can, if they want to enough, hack all data on your PC.
Paranoia runs deep Into your heart it will creep It starts when you're always afraid Step outta line, the Man come and take you away ~ Steven Stills and Buffalo Springfield, 1967
You are vulnerable when you enter networks, they can steal info by means of router data leaks, IP address hi-jack or by other means such as intercepting traffics from the cable boxes in your neighborhood. http://securitytracker.com/alerts/2008/Mar/1019715.html http://lists.jammed.com/vuln-dev/2001/04/0116.html
I think the best answer to the OP's question as been given by Agyar. It can also be added that, if your intention is to defend against traffic analysis, and want a - relatively correct - anonimity, you can either connect from an "internet cafe" here and there, or more simply (and way more slowly) connect thru an onion router, like the well know Tor.