I was trying to get Ubuntu (6.10) to hibernate, without much success (remember, I’m a Linux newbie). One of the side effects of the experiment was that Ubuntu did not recognize my swap partition any more (probably because during the hibernation-attempt it was overwritten with some random data from memory).

If you find yourself in a similar situation, you can run the Gnome Partition Editor, by typing in a console sudo gparted or pressing Alt-F2 and typing gksudo gparted. You should see an unknown type partition in the list. Delete it and (re)create a partition with type linux-swap in the free space. Now reboot your computer. This should solve the problem.

Warning! Using the partition editor, you can seriously damage your computer and lose data! Only use it if you know what you are doing!

Update: please read the followup on this advice.