There is no privacy.
The only thing that stops me from carefully decipher your identity by analysing your IP address and browsing behaviour on my site is that I have better things to do in my spare time. However, if I ever have too much time on my hands, be prepared that the trace you leave behind in the log files is scrutinized.
If you don't like it -- quickly, go somewhere else! (like Google, which keeps even more info, and actually uses it)