If your government isn't yet on the verge of an Internet shutdown, your best defense to keep the Web running at your house is to do some preventive care for your Internet connection. Plenty of tools are available to let you browse the Web without Big Brother (or, more commonly, big-box stores) looking over your shoulder.
The first and easiest tool to use is , which employs a routing protocol that makes it easy to stay anonymous on the Internet. Tor sends your communications through other users' networks, allowing you to browse and chat in relative anonymity. Tor is already used by journalists, civil liberties groups, and even the U.S. Navy for anonymous communication, and it has even been helpful in the recent debacle in Egypt.
If you're looking for something a bit more heavy-duty, is a software package that allows you to hide your IP address for about $80 a year. Anonymizer is a bit different from Tor, in that Tor hides your IP address through a distributed network, while Anonymizer has a dedicated server to help disguise that address, along with a Website that shows just how much information the address alone gives away.
For extra credit: You can find plenty of tutorials around the Net that show you how to keep your privacy online, including articles on PCWorld.com. We've covered how to for instance. Also, check out from Instructables on blocking nosy RFID chips.