An error has ocurredJSPlugin.3005
Install the latest cumulative IE update :
http://www.microsoft.com/en-us/download/details.aspx?id=45134 （32 bit）http://www.microsoft.com/en-us/download/details.aspx?id=45154 （64 bit）
I found the cause for this problem. I upgraded Internet explorer directly from IE8 to IE11. So I got the above said error during debugging.
Then I downgraded Internet explorer from IE11 to previous one(IE8). Then upgraded IE8 to IE10. Again upgraded IE10 to IE11. Now the debugger for IE11 is working fine.
Just a small update for Season714's answer if you're using Windows 7:
M$ did some magic things cause Windows 7 Updates take forever, so before you install those IE updates, you have to disable your network adapter first.
By doing that, that update installation will start in few seconds and the error will be fixed. But if you don't, Windows Update will run first and it would take forever to complete.