The release date of Project Natal is to be announced today (13th June 2010). The GAME website currently has a timer ticking down and at 7pm we will know when to expect Natal. You can place a deposit through GAME to pre-order it now. I will update this article with the release date(and price if that is confirmed too) as soon as the details are out.
EDIT: The countdown has ended(and gone into negative numbers). Those who pre-ordered Natal should soon get an email confirming the release date. As soon as I get confirmation I will place the date here.
I have been informed that a date wasn't supplied like it was said to, however that could be announced at the Microsoft conference. However, it has been announced by Microsoft that Project Natal is now named as Kinect. It also seems extremly likely now that a smaller Xbox 360(maybe Slim) might be released alongside Kinect and/or bundled with it. With the Microsoft conference so close I imagine there would be some mention about this. The launch event for Kinect was yesterday, and featured Cirque De Soleil. Numerous games for Kinect were also shown.