"Hibernate" in the windows world meant suspending memory contents to disk and powering the machine completely down. Apple has always taken a more fluid approach of copying memory contents to disk, but leaving power on for the fastest wake time (unless the power source is lost, in which case the copy on the disk is used to restore the session instead.) In OS X this is enabled by default on portables- it can be configured using pmset in the terminal.
On my Pismo G3 running 9.2.2, the 'Energy Saver' control panel contains a section for 'Sleep Options' in the Advanced Settings tab. There's a greyed out box there called 'Preserve memory contents on sleep.' which I presume would enable Apple's style of hibernation in OS 9. Perhaps the Pismo does not support this feature in hardware, so I'll need to check my TiBook when I get back to town.
FWIW, my 5500 and TAM do not present this option at all in their Energy Saver control panels under 9.1. This could be because they're old-world models with less sophisticated power management, because they're desktop machines, or both. More data needed.