The Notification Center in Mac OS X Mountain Lion can be used to see a quick view of the day's events and actions. Unfortunately, users of Remember the Milk will not see their todo lists in the Notification Center, since it is a web service. But there is a way.
Remember the Milk provides a CalDav calendar that you can subscribe to in iCal. You can do this by logging into Remember the Milk and going to Settings > Info and copying the url for "iCalendar Events Service (All Lists)." Go to iCal and choose File > New Calendar Subscription and paste in the url. Now you have a calendar with your Remember the Milk tasks in it as events that will appear in the Notification Center.
It's not perfect. The subscription only has tasks which have a due date and you don't see the priority or any other information about the task. In practice, you generally want to see the most immediate and important tasks in the Notification Center anyway, so just make sure that those tasks have due dates.