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:
sudo pm-hibernate
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.