This simple to-do list app keeps your agenda synced across devices in real time, works with or without an internet connection, and supports both shared and private lists.
Note that you can access this app from the web just as easily as you can from an iOS device: http://todos.meteor.com/. Loading the app on more than one device simultaneously is a great way to see how your data syncs back and forth, updating the user interface in real time.
Meteor Todos will remain free to use forever.