The most commonly offered resolution to a non-available hibernate mode is to run "powercfg /hibernate on" at an administrative command prompt (to start it: Click "Start", type "command" in the Start Search box, right-click "Command Prompt" in the Programs list, and then click "Run as administrator").
Complicated - and not the right solution for most people.
I found out that it frequently has to do with the new "Hybrid Sleep" function in Vista. When this is enabled, hibernate is disabled. Since I don't care for "Hybrid Sleep", but rather prefer "Hibernate", I changed it to allow hibernation as follows:

Go into the "Control Panel". Then click on "Power Options" or "Change battery settings" under "Mobile PC" (depending on your Control Panel mode - whichever you see).
Then click on "Change plan settings" for the currently selected power plan.
Now click on "Change advanced power settings".
Then click on the "+" left of "Sleep", and then on the "+" to the left of "Allow hybrid sleep".
Now set both "On battery" and "Plugged in" to "Off", and click "OK".
Now you will have the hibernate function available to you.