This was disabled from 12.04 (Precise Pangolin) as users were experiencing too many issues. Here’s how to re-enable.
Firstly check you have enough swap space:
cat /proc/meminfo | grep "Total"
If SwapTotal is greater than MemTotal there’s a good chance you have enough.
Secondly check if hibernation works correctly on your hardware.
Save your work then run:
All going well the computer will hibernate and shutdown. Restart the computer then verify everything has restored correctly.
Thirdly, if hibernation works, go ahead and restore Hibernate to the menus:
sudo nano /etc/polkit-1/localauthority/50-local.d/com.ubuntu.enable-hibernate.pkla
Make sure it contains:
[Re-enable hibernate by default] Identity=unix-user:* Action=org.freedesktop.upower.hibernate ResultActive=yes
Reboot and the menus should be updated.