My favorite is Chrome’s web inspector. It’s always there, does not require extra software, It just works.
I also use Safari’s web inspector, but it not as easy. I use firebug when I need to debug something in firefox. I muddle through Opera’s debugger when I am feeling particularly masochistic. I sometime use IE9/10’s debugger when I need to figure out why IE is doing something different.
A successful debugger has all of them at his/her disposal.
JΛ̊KE