With Firefox 3, I used an <embed> tag to add Adobe's plugin to my Ajax app. When removing the element from the page/DOM, the browser would just crash, closing all the tabs and leaving me with the Crash Report window. This would not happen without Firebug.
I don't understand what causes the crash/instability. The issue at the time was constantly reproducible on Windows machines with FF3 and would not appear with Firebug disabled or Acrobat disabled. Altering a property of the <embed> would crash it sometimes, and removeElement() would always crash it, but after a variable amount of time after removeElement() was called. No sign of CPU usage or memory leak, the browser just disappeared.
To fix this issue, I had to replace the <embed> tag by an <iframe> tag. This might cause different other issues depending on the setup of your Acrobat plugin (e.g. a download popup) but will avoid the crash.