I use Chrome, or when it doesn't want to work, I use Firefox as my backup. LAST resort is Internet Explorer.
Mozilla Firefox as always, hands down! But for smartphones or tablets I use the Google Chrome app for the internet browser.
I was a long time fan of FireFox until I came across Google Chrome recently and now I'm a Chrome fan. I left FireFox because I couldn't take their memory hogging anymore. I still keep Internet Explorer and use that when I need to check Windows Live (I want to see the updates rather than have them install automatically).
As i type im using Firefox but i tend to use Ice Dragon which is a secure Web browser based on the same open-source browser engine that powers Mozilla's Firefox.. More Info - IceDragon