I've seen laptops which have Hibernate at the Start menu instead of Shut down, and I find it very useful. How do I enable it at my desktop?
You should be able to do both on any computer. If you press the little right arrow next to 'Shut Down' it will give you a list of other options.
If you want to change it so that the default action is Hibernate as opposed to Shut Down, then;
Right click the start button, click 'Properties' and change 'Power Button Action' to whatever you want it to do.
Hope that helps.