I don't know whether chrome or IE has got this as iam not using it. This option is available in firefox as well as Epic Browser and can be enabled by selecting Tools -> Start Private Browsing. In this mode, history,cookies and other things are not stored.This option can be turned on when we are using public or shared computers or when we are doing any financial transaction.
Switch to Private Browsing Mode Easily with Toggle Private Browsing
Looking for an easy way to start and stop Private Browsing Mode in Firefox? With Toggle Private Browsing, you can switch back and forth with a single toolbar button.
Get the Button Set up
First install the Toggle Private Browsing extension and after it is installed, right click on one of your toolbars and select “Customize”. Once the Customize Toolbar Window has opened, grab the Toggle PB Mask button and move it to the toolbar location that best suits your needs.
Once you have the button set where you want it, it is just a matter of clicking on it to start and stop Private Browsing Mode. Notice that the “Mask Button Color” is lighter black at the moment.
Options
There are two options available for the extension. To “Auto-start in Private Browsing Mode” and “To disable the Private Browsing Mode prompt message”.