If you were used to put your Mac into hibernate mode using the free Deep Sleep Widget you were out of luck after upgrading to OS X Mountain Lion. The widget was still able to put your system into hibernate mode but after starting your computer again all you got was 3 beeps followed by a normal reboot of your system.
As the Deep Sleep Widget is open source I had a look at it and was able to fix the widget for Mountain Lion.
Get the current version here.
Extract the archive and start the installation by double clicking the widget.
It should run on all Intel based Macs and I've tested this version on Snow Leopard and Mountain Lion. If you were able to run it on a different OS version it would be nice if you leave a comment here.