I am running OpenSuSE and when I close mine it goes into standby. although standby also shuts off XMMS so the music I was listening to goes off.
SuSe uses a powersave daemon as part of the acpi. There is even an app in KDE called Kpowersave.
Whatever you do, don't choose suspend to disk. Hehe it copies everything to swap then shutsdown he harddrive, and the only way to restart is by hitting the power button. And may or may not result in corrupted data.
The best I have been able to do is either get the a blank screen saver or suspending the system. Hopefully someone knows how to fix the problems.