TechCrunch claims that Apple has notified developers that the debut iPhone applications will be available for download on the iTunes App Store at around 9am PST Thursday (July 10th) morning. We haven't heard verification of this, but due to the midnight New Zealand launch, it seems likely the App Store will be live by then.
More specifically, that is the point at which the NDA restrictions will be lifted and the press can begin writing about specific applications that will be offered through the online store. It is believed that the App Store will effectively go live and the the iPhone 2.0 software will be released at that point.
We will provide further details on this as they become available.
Update: Forbes also believes that the app store will a launch around 9am PST on Thursday.