How do I stop PyCharm from autocompleting class methods?

The option is located at:

Settings > Editor > Smart Keys > Insert Self...

EDIT: As of pycharm 2017.1 it's under File -> Settings -> Editor -> General -> Smart Keys

Go to File > Settings (or Ctrl+Alt+S) > [IDE Settings] > Editor > Code Completion.

The "Autopopup code completion" setting will determine if the popup opens automatically. Below it, the "Insert selected variant by typing dot, space, etc." is likely the setting you want to turn off.