There is a program called pm-is-supported that can be used to check for the suspend capabilities of the system.
On my system here are the results (0 means supported, 1 means unsupported):
$ pm-is-supported --suspend ; echo $?
0
$ pm-is-supported --hibernate ; echo $?
0
$ pm-is-supported --suspend-hybrid ; echo $?
1
The manpage of pm-is-supported suggests that s2both supports hybrid suspend. I've installed s2both, available in the uswsusp package but it still reports that hybrid suspend is not supported. I have a hunch that it needs a reboot because it updated the initrd image. I'm gonna reboot and report back. Wish me luck.
Update: Running sudo s2both wrote the snapshot to disk and suspended to RAM correctly, however when I pressed a key to resume the system rebooted (and didn't restore the snapshot from disk).
I think there's something wrong with the uswsusp package in ubuntu. The splashy package (which is used by uswsusp) has a file conflict with lsb-base which has been left unfixed since Jaunty ( https://bugs.launchpad.net/ubuntu/+source/splashy/+bug/328089 )
Try running sudo s2both or sudo pm-suspend-hybrid, see if it works on your system.