Is it possible to remove the border (and titlebar) of a window?

I plan on combining this with moving the window to a certain monitor and resizing it to fill the screen.
(And maybe setting it to always on top)
That way it should look like a full screen application.

This would be useful for applications that don't support fullscreen or applications that only support fullscreen on the primary monitor.

I'm sure there will be other uses for borderless windows.