IP addresses can identify you down to a town close to where you are depending on your ISP. For example, is someone gets your IP address (from you visiting a web site for example), they can perform a reverse lookup on that address and find something called a host name.
If you look at, this is a random IP, 24.12.12.12 you will see the host name is: c-24-12-12-12.hsd1.il.comcast.net.
This shows that the user of that IP is using comcast and is probably in Illinois (given by the IL).
The UK ISPs appear to get you closer to the end user, with the broadband head ends actually giving small town names.
If you have a static IP address, one that doesn't change a lot, then Google comes in handy. Try searching for your IP address and see what comes up. If a forum you post to displays your username and IP on a post then you have got a step closer to the person as you now have a handle as well as an IP address......search engines, social networking sites etc can always trip you up thanks to a few postings you made a few months ago!
To find what your current IP address is, use sites such as http://whatismyip.com or http://displaymyip.info
Proxies will help you cover your tracks a bit but some may also send information about your IP address as well as the proxy IP.
Hope that helps!