Is there a way to add, read, or delete reminder items from the new iOS 5 built-in Reminders app?
This will be all possible with iOS 6! :)
https://developer.apple.com/technologies/ios6/
At the time of writing this answer was sufficient. To keep it updated here is a tutorial which looks very useful for anyone developing an app which interacts with the native reminders app: Using iOS 6 Event Kit to Create Date and Location Based Reminders