A long time ago I installed the Art Directors Toolkit widget. Today, when I restarted my computer after a power outage, there were 2 instances of the widget. The first one is in the dashboard and a second appears on the desktop, like any other application would appear. I don't know how to remove it. It has none of the usual dashboard buttons and it reappears if I relaunch the Dock.
Apple allows widgets to be displayed on the desktop in order to allow the people developing the widgets to test them without using Dashboard. Your system must have had that capability turned on somehow and that widget set to run on your desktop.
It's very easy to get the widget off of your desktop, and make it so that no other widgets will accidentally be relocated.
To get the widget off your desktop: click and hold on the widget, then press F12 to enter Dashboard. Once Dashboard is active, release the mouse from the widget. The widget is now docked in your Dashboard instead of on your desktop.
You'll probably have two copies of the widget in Dashboard now. You can get rid of one in the normal way (press the plus button at the bottom left and click the
(x) on the widget).
You can also just hold down the option key over the widget and the
(x) will appear.
Now, to prevent other widgets from escaping Dashboard in the future:
Open Terminal (/Applications/Utilities). Paste this in and press enter:
defaults write com.apple.dashboard devmode NO
If, on the other hand, you want to run some widgets on your desktop, you can run the above command with
YES instead of
Then, activate Dashboard, click and hold on a widget, exit Dashboard, and release the widget.