Anyone who IS paranoid enough to worry about people knowing their IP could investigate the use of anonymous proxies, and software like JAP which can bounce each packet off a different proxy, thus making tracking traffic to/from a site very difficult. Or, you could go further and use something like Stealthier http://www.photono-software.de/Stealther/main.php3?language=eng&reseller=
Yes, people can still track you if they REALLY wanted to, and if they have the time and skills, but it can certainly make things pretty tricky.
And, if you wanted to obfuscate which browser you're using, try Proximotron, which can filter all packets to/from HTTP sources and change the header info such that the site can be fooled into thinking your using any browser you like - even non-existent ones.
Cookies can be stopped/controlled using the tools in IE or again using the Proxomotron to "spoof" cookies if sites refuse to work without them...
And you thought tracking people on the net was simple?