Generally, Macs only hibernate (storing the existing system state to disk and powering off) when the battery has gone to nearly absolute zero. At all other times, they sleep -- meaning that the existing system state is stored in RAM, and the machine goes into a low-power mode. The reason for this is that it takes longer to restart/restore from hibernation state. But having the machine fully off does save battery life.
Since the MacBook Air's solid state drive (if you have a model so equipped) has exceptionally fast startup times from disk, hibernation restores are very quick (five or so seconds, in my experience). Also, hibernating all the time will save you battery life -- again, in my experience, up to ten percent longer run times. YMMV.
Numerous utilities are available to change the default low-battery mode to hibernate. I like Jinx's Smart Sleep, which installs as a pref pane and is Snow Leopard compatible.
Remember, if you're hibernating, you use the power button to "wake up," rather than just hitting a key on the keyboard.
[robg adds: You can use this tip on any machine with an SSD, if you're willing to put up with slightly longer "wake" times.]

