Chrome's browser privacy feature is called Incognito. The browser does not track what you are viewing which means it does not create a retrievable file that lists the pages you viewed or searches you submitted. The viewing experience will be "normal" though all extensions will be disabled. Extensions include custom toolbars and applications such as antivirus software and Skype. You can enable the extensions if needed.
When you open a browser window in INCOGNITO you will see an explanation similar to this screenshot.
Internet Explorer 10 (IE10) offers browser privacy in the form of its InPrivate Browsing mode, easily activated via the browser's Safety menu or through a simple keyboard shortcut. With InPrivate Browsing active, IE10 does not save any private data files such as cache and cookies. Browsing and search history are also wiped out while using incognito browsing within Internet Explorer.
Firefox offers this info on their Private Browsing.
Warning: Private Browsing doesn't make you anonymous on the Internet. Your Internet service provider, employer, or the sites themselves can still track what pages you visit. Private Browsing also doesn't protect you from keyloggers or spyware that may be installed on your computer.