How can I automatically clear my browsing data when I exit Chrome? I don't like having my searches and web history hanging around forever. Therefore, I wonder: Is it possible to automatically clear browsing data on exit in Google Chrome? If it cannot be done with Chrome, do you know of any other good web browsers with this capability?

P.S. I am not willing to root my device just for this purpose. Therefore, I'm looking for a solution which does not require root access.
I would use firefox. It has an option to clear on exit. You do have to go to the menu (which you can access by tapping the menu icon) and hit quit every time, but seeming as there is no way I know of in chrome, It's better than nothing. Firefox does take some getting used to though, so switch with caution.