As many people have pointed out, Gutsy doesn't suspend/hibernate well due to some kernel changes in version 2.6.22.
Khurrum1990 suggested in a bug report to try installing Hardy's kernel. So I tried that and suspend works immediately, hibernate requires a little tweak.
Below is instructions on how to install the kernel. Note, for me, there's a side effect with this new kernel on a Gutsy system, my sound quality became poor when using this kernel. You can test it out and see whether you get this or not.
OK, first, you will need to download the package. The packages can be downloaded at:
http://archive.ubuntu.com/ubuntu/pool/main/l/linux/linux-image-2.6.24-2-generic_2.6.24-2.4_amd64.deb
You will probably want to install the restricted modules as well so you can continue using nVidia graphics drivers, so download and install the following two modules as well:
http://archive.ubuntu.com/ubuntu/pool/restricted/l/linux-restricted-modules-2.6.24/linux-restricted-modules-common_2.6.24.2-2.8_all.deb
http://archive.ubuntu.com/ubuntu/pool/restricted/l/linux-restricted-modules-2.6.24/linux-restricted-modules-2.6.24-2-generic_2.6.24.2-2.8_amd64.deb
Once you have installed the above modules, you will need to edit the acpi-support file.
In a terminal, run
sudo gedit /etc/default/acpi-support
Then search for
POST_VIDEO=true
and change that to
POST_VIDEO=false
Lastly, search for
HIBERNATE_MODE=shutdown
and change that to
HIBERNATE_MODE=platform
Save the changes, then reboot and make sure you run the new with the new kernel. Now you should be able to suspend and hibernate your system.