Ubuntu 12.04 doesn't have enabled hibernate feature by default, but you can enable it if your hardware has support for hibernation.
Before you turn on the hibernate option in Ubuntu 12.04 Precise Pangolin you need to be sure that you machine supports hibernate without any issues. Please consider that hibernate feature on unsupported devices could make a lot of problems even losing your data. You're warned!
How to check if computer supports hibernate in Ubuntu 12.04
To be sure that your computer can hibernate open the terminal and enter the command:
Enter your password when prompted.
After you computer turns off, switch it back on. If all windows appear as they were before restarting and the system continues to work you can consider enabling hibernate.
In case that hibernate doesn't work properly be sure that swap partition is at least as large as available RAM.
How to enable hibernate in Ubuntu 12.04 Precise Pangolin
1) Create file
2) Add the following content
[Re-enable hibernate by default]
3) Save the file
4) Restart machine
5) You should see new menu item that will allow Ubuntu hibernation