Vista WinCal has a feature where you can set appointments to notify even when the app is not running. It uses Task Scheduler. Thing is I've found it to be unreliable. Not good for a calendar app. The file would fail to fire in the Task Scheduler due to corruption or some other error.
Basically I'm looking for a simple calendar where you set an appointment and close it. When the due date/time comes around it opens and notifies you. I'm only looking for a free one.
I've found some nice looking calendar apps on Softpedia but be they simple or complicated they seem to need to be running to notify.