Apple has updated MobileMe Calendar application, that now include alerts feature. Like, an iOS device or the Mac's calendar application, me.com will now allow you to set alerts for calendar events.
Any alert you setup on me.com will automatically sync to your other MobileMe devices. You can choose to be notified 5 minutes, 15 minutes, 30 minutes, 1 hour, 2 hours, 1 day, or 2 days in advance of your event.
If you are on MobileMe Calendar application at the time scheduled alert, you will appropriately be notified, as shown below: