By default, there is no Hibernate item anymore in Ubuntu 12.04 menu. The reason is that some computers are just not compatible with that feature so that you could lose your data.

You should therefore only use the Suspend feature. Note that suspending your computer still requires a little bit of energy, and if your battery gets empty, you will lose your data. If you really need your computer to hibernate, the command is:

sudo pm-hibernate

However, on my laptop, I get the following error: Not enough free swap.
This is clearly a bug since I only have 2GB of RAM but 4GB of swap. A way to solve this problem is to install uswsusp:

sudo apt-get install uswsusp

Once installed, you can hibernate by executing s2disk:

sudo s2disk

Actually, the command pm-hibernate should also work now since it should execute s2disk.