Mind you, if it's not a trustworthy proxy site, they might be registering everything you transmit, such as passwords and such, afaik.
Depending on the country the proxy is in, I think they have to, don't they? Part of the wave of "omg, hackers use these things, ban/regulate them" thing.
There's nothing you can really do by hiding your IP address for security concerns. If someone is desperate to find you then they will - be it hackers or other governments. But as long as you're not doing something you shouldn't, you don't need to hide your IP.
