Things that sometimes check the internets without you knowing (when you log in):
- System Clock (synchronizes clock)
- System Update (checks for any updates, especially if you've had your computer logged off for a while)
- MSN Messenger
- Any proggys you see in your task bar (ones that start up automagically)
It's not a bad idea to do regular virus/spyware checks anyway. Assuming you're on windows, Microsoft Security Essentials works great and it's free (
http://www.microsoft.com/security_essentials/). Often does better than other free and some paid anti-viruses.
As well, Spybot S&D is still great for getting rid of spyware (
http://www.safer-networking.org/en/download/index.html)