It was bound to happen. The first discussion threads fill up with Xbox 360 owners complaining about crashes and shutdowns. Possibly there is an overheating problem.

It is not clear what causes the crashes or shutdowns. Maybe some consoles are placed in a poorly ventilated place, or maybe there is an issue with some of the consoles or the power supplies. The discussions are growing, but it does not look like an epidemic just yet.

It would have been close to a miracle if none of the shipped Xbox 360 units would have a problem. Maybe this could be the 11th top reason not to buy an Xbox 360.

Update:
Microsoft responds to Xbox 360 Crashes
See the following Xbox 360 discussion boards for the reported Xbox 360 crashes and problems.
xbox- scene
team xbox
Here is a tip on potentially fixing the 3 flashing red lights on xbox.com

A Xbox 360 user posted some screen-shots of his crashes on flickr.
See also coverage on Slashdot.