If you were lucky enough to get an order placed for the Moto 360 on Motorola's website before they went out of stock, keep an eye on your email. Motorola has already gotten some orders out the door at its Texas facility, with an expected arrival date of Tuesday, September 9th.
This first wave of shipments will probably be followed by a bit of a dry spell. Best Buy won't have any units in stores until September 14th and online stock is sold out. Google Play had stock briefly, but has now pushed the shipping date to 2-3 weeks. Motorola is sold out and doesn't list a restock date at all, but there's an option to sign up to be notified when it's back. Of course, this is all still US-only. Sorry, rest of the world.
Update: It looks like Best Buy has started shipping units as well.
[Thanks, remister, Luke Olson, and Nick]