On my home computer, I am a die hard Firefox user. I was never a big fan of Google Chrome and Internet Explorer is just, well a bit dated.
On my mobile phone I tried the default Android browser and later switched to Opera. However, I found them to be slow and clumsy to use. After doing some research I found the Dolphin HD mobile browser. And although I don't quite like the name, I love using it.
It is simple, intuitive, fast, and tends to play Flash content better too!