As far as I'm aware of, Tor is the only decent free anonymity service for hiding your IP, but its performance is very limited. For browsing, it may perform no better than 56k dial-up like speed. As far as I'm aware of, it can be used for anonymous P2P, but don't expect to be able to download or share large files quickly over it.
The main problem with the free ones is that very few users or companies are willing to provide the bandwidth to run the services. Most other free anonymous services actually make the use of public proxies which are often run by PCs infected with malware running them as proxies without the user's knowledge.
For P2P file sharing, you will need a VPN based service compatible your file sharing software (e.g. BitTorrent.) The only reasonably priced one I know of off hand is Ipredator, which is â‚¬15 for 3 months. As far as I can tell, it allows incoming connections also, which is something no free anonymous service I'm aware of is capable of, which makes it better suited for file sharing heavily dependent on incoming connections such as BitTorrent.
If you would like to be able to get around regional restrictions, e.g. watch online TV services outside of the region they are restricted to, you would be much better off paying for a country based IP cloaking service. For example, Identity Cloaker gives you an IP from a country of your choice, so if let's say you would like to watch TV shows online restricted to UK viewers, you would select a UK IP. Their service is free for a few websites, e.g. Google, Blogger, Twitter, Facebook, etc. so you can try it out to see what its performance is like. It's quite pricey at â‚¬30 for 3 months, but has the major advantage of letting you choose which country to spoof your IP to.