If HTTPS Everywhere still stores too much information for your taste, try . The system was designed for the US Navy to protect government communications, but now is available for use by the public. It鈥檚 a free download that makes all of your online visits anonymous. The downsides are that it slows down your browser.
If you want insurance of browsing security, nothing is full-proof, but Tor comes pretty close to it.
Check out this from the Electronic Frontier Foundation that shows the differences between using Tor and HTTPS.