Faced this bizzare issue today in Firefox. Firebug was opening automatically for all pages. Even on closing firebug, all I had to do was click on a new link in the same tab for it to appear again. This happened for all tabs.
Turns out I had accidently turned on “On for all Web Pages” option. Right clicked on the Firebug icon to turn it off. Problem solved 
Right click Firebug to disable "On For All Web Pages"