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 :D
[caption id="attachment_246" align="aligncenter" width="300"
caption="Right click Firebug to disable "On For All Web Pages""][/caption]