Of course, your internet service provider still knows where you go, and the government can just request that information. There are a few ways around this. The easiest is with a web-based proxy like KProxy. Load any website in Kproxy's URL bar and the site routes your request through another computer.
Your ISP won't see what site you're really visiting, and the site you're visiting won't see your real IP address. The catch is that proxy sites can often load pages slowly.
Downloadable proxy servers can be a bit more reliable. Two popular ones are Tor and Privoxy. These not only re-route your traffic but encrypt it, too. TAILS is another helpful tool for browsing privacy, but it can be a little tough to set up.
I should note that while these tools obscure your web travels, don't think you can get away with any wrongdoing online. If you engage in illegal activity, rest assured that law enforcement can and will find out about it.