If you’ve been successfully running 16.04 with your video driver before, but the login loop issue happens after the latest software update, try this, it worked for me after trying EVERYTHING else. This is the equivalent of searching for “additional drivers”:
sudo ubuntu-drivers list
sudo ubuntu-drivers autoinstall
For me, this updated the driver for my nvidia quadroFx 3800 in a way that using
sudo apt-get install nvidia-current would not.
I ended up installing nvidia-340.
After autoinstall, invoke another tty (ex. ctrl+alt+f1) and
sudo service lightdm restart