I'm trying out a lot of linux distros so I have many paritions. However Ubuntu is my working distro so it would be nice to have hibernate working for it. Do I need a swap partition as large as my RAM to be able to hibernate? I have 2gb of RAM and less then 2gb of free space / . If the anwser is yes then do I need to disable other OSs from using the swap partition to avoid corrupting the Ubuntu hibernate? Would I notice any performance differences without a swap partition? Worst case what happens if I don't have a swap partition and all RAM is used up?

Do I need a swap partition as large as my RAM to be able to hibernate?
Yes.

If the anwser is yes then do I need to disable other OSs from using the swap partition to avoid corrupting the Ubuntu hibernate?
Yes.

Would I notice any performance differences without a swap partition?
Doubtful; two gigs of RAM is more than enough for anything except lots of picture/video editing.

Worst case what happens if I don't have a swap partition and all RAM is used up?
Non-system processes get killed.