Constant prompts for FaceTime Password, iCloud Password and iMessage Password I don't use any of these services. Currently there is a dialog box permanently on the screen prompting for a password. If I press cancel, it's replaced instantly by another dialog box, prompting for a password for one of these services, apparently randomly chosen. 

Sometimes, it's the same service several times in a row. Sometimes there is a pause of maybe half a second before the next dialog pops up.

Is this a known issue with Mavericks? It's a 2014 rMBP.
I had same problem on my i-phone 6, so  went into 'Settings' and turned 'Facetime' off!  I don't use Facetime, so it seemed the best way to get rid of the annoying pop up.