Some browsers, like Firefox, have a "privacy mode," allowing users to surf without the browser saving information. This only works on the "local level," which is to say that your company's IT employees know exactly what you're up to, you still have no privacy protection, and your IP address is still hanging around. Most browsers call this Private Browsing; Chrome calls it "incognito."
Private browsing posts, Lifehacker
Private browsing, Firefox Help
Private browsing: it's not so private, Ars Technica
Open IE’s Private Browsing Mode the Easy Way, How-To Geek
How to make Safari’s Private Browsing feature actually private, Switching to Mac
How to Start Private Browsing Session in Google Chrome?, Techie Buzz