There has been continuing disruption to Apple’s online services throughout today 11 March 2015, and although some services such as iCloud seem to be functioning again, you are likely to experience all sorts of problems, including failure to authenticate with your Apple ID.
I won’t be surprised if this is some sort of an attack; it seems too sustained for an internal glitch.
It’s just as well the Watch didn’t start taking pre-orders today…
Update: as of 12 March, it looks like services have returned to normal. The official line was that it was a DNS problem. Really?!