one thing you could do is the ctrl-alt-del to see what is running on the system (and check them on www.answersthatwork.com) they usually
tell you whether its a valid program or whether you can get rid of it.

Id definitely use zonealarm firewall, ad-aware is handy too,
and norton with auto-update.

set your security settings to high on explorer as well, as there are java scripts, activex etc in some sites that may reset your homepage and the only way to get rid of them is to edit your registry.
(using regedit - and check default pages etc)

some programs actually require an internet connection so they can check that youre a valid user,

also lookup foistware on google and you can find out about questionable stuff thats installed on your computer without your knowledge (typically any program you install may install a whole bunch of junk you dont need)

I found out that onetouch multimedia keyboard was always checking my internet connection (because it has all these keys for sports shopping etc that I never use). THis was a default setting with hp pavilion computers, so basically everything you do on the net is redirected to hp.redirect.com (or something). A major violation of privacy as far as Im concerned.