How to stop annoying documentation popups in IntelliJ IDEA

Go to File>Settings>Editor>General - in the section 'Other', uncheck 'Show quick documentation on mouse move'.

In later versions of IntelliJ, the path is File>Settings>Editor>Code Editing, and it is under the "Quick Documentation" section.

In my cause, 'Show quick documentation on mouse move' was in Editor > Code Editing: