1. Tor only protects Internet applications that are configured to send their traffic through Tor — it doesn't magically anonymize all your traffic just because you install it. We recommend you use Firefox with the Torbutton extension.
2. Browser plugins such as Java, Flash, ActiveX, RealPlayer, Quicktime, Adobe's PDF plugin, and others can be manipulated into revealing your IP address. You should probably uninstall your plugins (go to "about:plugins" to see what is installed), or investigate QuickJava or FlashBlock if you really need them. Consider removing extensions that look up more information about the websites you type in (like Google toolbar), as they may bypass Tor and/or broadcast sensitive information. Some people prefer using two browsers (one for Tor, one for unsafe browsing). Torbutton provides many features to protect your anonymity. It can be safely used instead of many plugins, such as FoxyProxy or NoScript.
3. Beware of cookies: if you ever browse without Tor and Privoxy and a site gives you a cookie, that cookie could identify you even when you start using Tor again. You should clear your cookies frequently. CookieCuller can help protect any cookies you do not want to lose.
4. Tor anonymizes the origin of your traffic, and it encrypts everything inside the Tor network, but it can't encrypt your traffic between the Tor network and its final destination. If you are communicating sensitive information, you should use as much care as you would on the normal scary Internet — use HTTPS or other end-to-end encryption and authentication.
5. While Tor blocks attackers on your local network from discovering or influencing your destination, it opens new risks: malicious or misconfigured Tor exit nodes can send you the wrong page, or even send you embedded Java applets disguised as domains you trust.