After a slight delay, the new Xbox Dashboard has begun rolling out to 360 owners around the world. Or, well, it would be, if Xbox Live wasn't down for many of them. So be patient!
Those of us at Kotaku still awake can't connect to Xbox Live at all, and Microsoft's support website carries a ton of service alerts for the platform, the most important being a warning that users "may" experience difficulties doing the following:
Signing into Xbox LIVE from an Xbox console
Signing into Games for Windows — LIVE on a PC
Signing into Xbox LIVE from Xbox.com
Signing into the Xbox LIVE forums
So, yeah, the four most important things on Xbox Live.
The outages are most like just a temporary thing caused by millions of people trying to download the new dash all at once, so if you can't get the new dash (or play online), give it 10-15 minutes and try again.