iOS 4 supports Local Notifications
Apple - iPhone 4 - Multitasking done the right way
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Receive push and local notifications.
Third-party apps and services can send alerts and messages directly to your phone. So you can get sports scores, news updates, game requests, reminders, alarms, and more the moment they happen, without having to open the app that’s providing the notification."
There are currently Reminder apps that have local Notifications, no Push required.