When I have a choice, I use Lunascape. I used to use Opera, but when they did a dump and rewrite some versions ago, it lost everything which made it different (and which made me like it). So, now I use Lunascape, which is the spiritual successor to the Classic Opera. Heavily influenced by classic Opera, and, as far as I know, the only major browser supporting MDI.
On Linux, Konqueror is my browser of choice.
As secondary browser, I use Chrome or Chromium, and occasionally Iron.