Tor might achieve what you want, but it will be slow probably.
If you want true anonymity use a vpn service.
It's been some time ago, over a year, way before the snowden and nsa deal, that I made a post about anonymity. I almost hate to mention it because it almost ended up in me getting banned from here, but the post is still up to read here
Anyway if you want a good vpn service I would recommend vpntunnel.se It's a swedish based vpn service with multiple servers in multiple countries. After what came to light about NSA (things I already suspected) I can understand why a person might want to use such a service. They have two services (or you can buy both for a bit more). They support PPTP vpn, which is a protocol that most devices (computers and mobile) support natively. They also support OpenVPN, which requires their client software, but you get much higher bit encryption, you can pick the country you want to connect to, and some other features. It is also probably easier to use their client software for the novice user because you don't have to deal with configure PPTP settings. Just install the program, launch and sign-in.
Some things to be aware of. Some of the countries your connection terminates might cause red flags with different services. In my case it was gunbroker. I had used the VPN to connect to internet and was on gunbroker, logged into my account. They observed my account was logged into from a country other than what my account was registered. Nothing is to say I wasn't actually in that country as I do travel, but they froze my account and threatened to ban me. I wasn't trying to do anything illegal and my account was not compromised, I was just using the VPN to get around a content filtering device in this case.
A lot of the flak I got was people automatically thinking I must be doing something illegal if I wanted to "hide" my traffic. Say what you will, but I don't want the government or anyone else watching my every move even if I do have all my ducks in a row. Unfortunately you cannot trust them anymore to mind their own business so you may decide to go a route that keeps your business your business.