I have already set in the Energy Saver of System Preferences that
Computer sleep: on Battery Power, Never when plugged in, Never
so if I close the cover of the Macbook Pro running Mountain Lion, so that it sleep, then if I open up the cover within a few hours, then it wakes up right away -- which is all fine. However, if I open up the the cover and not touch it, then after some 12 or 24 hours, then it will wake up from hibernation, taking about 2.5 minutes before any password can be typed in. (update 2015: this Macbook Pro was running with a non SSD hard drive. The wake up time is a lot better if it is an SSD drive).
This is all when the Macbook Pro is plugged in (powered by the power adapter). Is there a way to make it not hibernate?