First, ensure you have more swap space than RAM (1.5 - 2x RAM as a guideline), using the command:
If you don't have enough space, follow the instructions here before continuing.
Once you are sure you have enough swap space, if hibernate still isn't working, install the powermanagement-interface package, using:
sudo apt-get install powermanagement-interface
This got hibernation working on my machine, I hope it helps you too.
Update: Make sure you check out Part II of this post, should this post not help you fully resolve your hibernate problems.