Although no ETA has been provided, Microsoft is aware of and working on sign-in and other issues affecting Xbox Live today.
Xbox Live members are currently struggling to sign into the service across all platforms.
On top of the service wide issue, an problem specific to Xbox 360 is causing problems utilising video or music content.
Finally, Xbox.com is being super patchy, and posting to the Xbox Live forums is pretty hit and miss.
Microsoft acknowledged the Live-wide sign-in issue in an update riddled with exclamation marks, which I have edited out to preserve my sanity:
"For our members that are currently unable to sign in to their Xbox Live accounts, we’re right here with you," the statement noted.
"We’ve got our team engaged and they are working hard to get everything back to normal as expediently as possible. You’re being so patient while we're working, and we really appreciate you. We’ll update you on our progress as soon as we have more information."
Keep an eye on the Xbox Live status page for the most timely information.