My password has been rejected. I reset my password, but I yet to see if it works.

I can't log in using an appleid from my iphone, but can with iTunes on MacOS.

Just talked to Apple and they have confirmed their login servers are not functioning. They suggested checking again in 2-3 hours.

Reset my password and can now receive mail.

It now works for me. Apple status page shows as fixed.
 

IAccording to Apple's System Status webpage, the iCloud issues began a little before 2 p.m. Pacific, a few minutes before the company released the latest Mountain Lion update. "

So NOT related to upgradoing a local computer to 10.8.3.

Had the same problem. Here's the fix that worked for me.

I did this after resetting my Apple ID password. Once i was logged in via the System Preferences panel then i could login to icloud.com with my new password.

Mail kept asking for my password on one of my 5 macs. The others had no problems. I checked the settings for Mail on the failing mac and the iCloud account and found authentication was by Password. I switched to to Apple Token and everything was fine after that. Go figure.

Just installed 10.8.3 (8:12 pm, EST) and iCloud broke. Mail works fine on other Mac that is still on 10.8.2. Seems the issue is not entirely fixed.

As an Apple developer I have been running 10.8.3 for a long time on several Macs and there have been many versions. Every one, including the latest has worked flawlessly with iCloud so I am puzzled by the number of folks posting about such problems. The better part of me believes they may have issues then the not so good part of me wonders if some of that missing Scamsung money is showing up.