Over night, so possibly after an update, my GUI login into Ubuntu 16.04 does not work anymore.
So I open another console (Ctrl+Alt+F3) and everything works fine.
I tried the stuff I found elsewhere: something with removing ~/.Xauthority.
In ~/.xsession-errors file I found at least the keyword, that others used to detect their errors: something with GLX.
In the end I did:
sudo apt autoremove nvidia-* sudo apt install nvidia-current
GUI login still does not work.
extension "GLX" missing on display ":0".
openConnection: connect: No such file or directory
cannot connect to brltty at :0
upstart: ..... ...