There are various ways to simply hide an IP:
http://www.anonymizer.com/
A hit via there shows as follows in my Apache log (rather than my real IP):
207.195.241.46 - - [22/Apr/2006:11:42:34 +1000] "GET /images/links.gif HTTP/1.1" 200 4660 "-" "Mozilla/4.78 (TuringOS; Turing Machine; 0.0)"
So (as the receiving end) I know the hit comes from an anonymized connection, but not where.
Another is:
https://proxify.com/ (also available as a Dashboard Widget)
A hit from there shows as:
66.98.130.120 - - [22/Apr/2006:11:46:33 +1000] "GET / HTTP/1.1" 200 9811 "-" "Mozilla/5.0 (Macintosh; U; PPC Mac OS X; en) AppleWebKit/412.6.2 (KHTML, like Gecko) Safari/412.2.2"
Another way is via The Onion Router:
http://tor.eff.org/
Each has pros and cons and all have a speed penalty.
Of course, you do need to understand that if you are an ISP who controls the router, you have greater levels of information about where packets are coming from, so some of the above tools may prove illusory and give you a false sense of privacy.
See:
http://privacy.net/ if you are interested in how much you are disclosing about yourself.
How much does all this matter? Who knows!