A quick glance at several international online Apple Stores (Canada and the UK for example) reveals that "June 7th" has been changed to simply "June." Shortages in the US have been regularly reported over the last week, perhaps as supplies are diverted to international customers. Even so, it appears that Apple is having trouble keeping up.
Meanwhile, we're hearing from eager customers all over Europe and Canada (who ordered early) that their shipping notifications have been triggered. Some Italian buyers apparently already have their iPad in hand. Also, the iBooks app is now reportedly appearing in the UK iTunes App Store.
If you're outside the US, UK, and Canada, what does your country's store say? Have you heard anything from Apple Store employees? Let us know.
Thanks to everyone who sent this in.