Can't log in to Hangouts I just uninstalled and reinstalled Hangouts to get the updated version. 
(Even though the market showed the new version, it didn't have "Update" yet).

Now, I cannot log in to Hangouts... it keeps asking me to add a Google account.
I've tried rebooting the phone, but no joy.

Gmail and other google apps still work fine, it's just Hangouts.
I've tried adding my account, and it tells me that it already exists on the device (which is true).
So this turned out to be a pretty easy fix, once it dawned on me what it was. 
I just recently installed the Xposed framework, and the XPrivacy module. 
When I uninstalled the old Hangouts, it must have deleted all the old permission settings in  XPrivacy, and then when I reinstalled it, it defaulted to maximum restriction. 

With access to the phone accounts restricted, Hangouts was not able to see my google accounts. 

The fix was as simple as fixing the permission settings for Hangouts in the XPrivacy module.