Open the menu
Window->Preferences->Java->Editor->Content Assist->Advanced
Now make sure the following are all ticked in the top and bottom sections:
Java Non-Type Proposals
Java Proposals
Java Type Proposals
Java Proposals
Java Type Proposals
Apply the changes and then close and re-open your project and it will build the autocompletions which will then become available when you hit Ctrl-Space.
I have Eclipse Luna. This didn't work for me.