The proprietary NVIDIA driver that comes with 16.04 seems to be problematic. I had problems with it, and I've seen at least one other question complaining of problems. This is what I did to solve my issue; it should work for you.
- Enter a TTY by pressing Ctrl+Alt+F1.
- Log in with your username and password.
- Run
sudo apt-get purge nvidia-* and confirm any prompts.
- Run
sudo apt-add repository ppa:graphics-drivers/ppa and then sudo apt-get update.
- Run
sudo apt-get install nvidia-364.
This will install the latest driver from that repository/PPA. It is a newer version than the one that comes with Ubuntu (361.42 vs. 364.15) and seems to be a bit more stable. It's also open source, so that's a plus ;-).
If you have any problems, or are confused by these instructions, leave a comment.