There seem to be a lot of excessive paranoia on this thread that, in all probability, requires some simplification.
The first thing to mention that it is the BPI (British Phonographic Industry) that go after British people that break copyright rules using P2P apps, the RIAA has no jurisdiction here.
Although some software claims to hide your IP address most of those have turned out to be smoke and mirrors, your IP address is always noted by the sites you surf and recorded by your ISP, i.e. time, duration, sites visited, data downloaded, uploaded, etc.
It has now passed into European law that your ISP must record and hold information, about your online activities, e.g. emails, IP address, surfing, from anywhere between 6 months to 2 years. I believe this law is something similar to the US's Patriot Act, at least the reasons for passing it were the same, i.e. fighting terrorism.
The BPI's policy in going after copyright infringers are slightly different to that of the RIAA, it's sister organisation, and can be readily read on it's website:
http://www.bpi.co.uk/index.asp
Still, it seems that lately the BPI have become more "gung-ho".
http://www.bpi.co.uk/pdf/Illegal_Fil..._Factsheet.pdf
The world of P2P is changing and it seems that the RIAA/BPI and their related organisations are determine to destroy it or change it forever. So it is incumbent on P2P users to change or modify their behaviour before being forced to.
UK Bob