1) Choices for P2P File Sharing: if your objective is to download/upload files anonymously, then there are services that will mask your computer's internet protocol (IP) address for a small fee, while still allowing you to use large bandwidth. The cost is usually a monthly fee or the purchase of a special software product.
These P2P-friendly services include Anonymizer.com, The Cloak, and A4Proxy. There is even a special non-profit project dedicated to P2P downloading anonymity: Mute Anonymity.
2) Choices for Web Surfing and Email Anonymity: If you are looking to avoid retribution for your political ideals, or wish to bypass the controls of an oppressive government in your country, there are free proxy and VPN servers available around the Web. But the most reliable anonymity choice is a special two-part freeware solution by the EFF to protect the democratic freedoms of private citizens. When combined, these two items "scramble" and conceal your online identity as a free public service. This anonymity platform is made up of Tor and Privoxy:
"Tor" and "Privoxy" is a combination "anonymizer" platform you install on your own machine. Tor is a special network of web servers run by the EFF and many volunteer server administrators. Privoxy is the software you need to connect to this Tor network.
The Tor Network and the Privoxy software work together to hide your computer's IP address. They accomplish this by bouncing your signal around several Internet servers called Tor "onion routers". Much in the same way Hollywood spy movies depict a telephone call being routed around dozens of false phone locations, so is your online identity when masked by these special Tor servers. Your true IP address is effectively hidden when you surf/email/download through the Tor onion network.
The Privoxy and Tor products are still imperfect, and they do not guarantee your anonymity. But as a start, Tor and Privoxy do reduce your exposure to surveillance, and make you 80% or more difficult to track.
Download and Configure Tor-Privoxy here.
Download Privoxy here.
If you are looking to add a layer of anonymity to your surfing/ emailing life, then try Tor-Privoxy. You will likely experience a somewhat-slower connection but your identity will be significantly more protected.
Remember: no masking of your address is 100% foolproof. And if you download/upload P2P files, remember that in any other country outside of Canada, downloading copyrighted movies and songs puts you at legal risk for copyright infringement prosecution.
P2P Downloaders, please note: the Tor Network was designed to protect private citizens personal privacy, especially in the important areas of Freedom of Speech, Freedom of Conscience, and Freedom of Democracy. Tor and Privoxy were not designed to help people download megabytes of movies and songs. Please do not abuse the Tor-Privoxy system by turning it into a P2P downloading avenue.
Furthermore, while the About Network actively promotes freedom of expression and the democratic use of the Internet, the About Network does not condone the illegal downloading of copyrighted files. If you are going to participate in P2P file sharing, please take the time to educate yourself about the legalities and consequences of such activity.
Warning to corporate/government users: if you hope to hide your unethical surfing habits from your own I.T. department, think again. The Tor Onion Network and Privoxy platform do NOT conceal you from internal surveillance at your office.
Next: How to Install and Configure Tor-Privoxy
Related: Understanding P2P and its Legalities