How to disable the small pop-up windows when mouse is over a Mathematica command in V10?

Unfortunately I cannot claim the original discovery, but there are additional CodeAssistOptions in M10, the one you want is:

SetOptions[EvaluationNotebook[], CodeAssistOptions -> {"FloatingElementEnable" -> False}]

You could replace EvaluationNotebook[] with $FrontEnd but I prefer not to change $FrontEnd options.

For what it's worth, the accepted answer does not function in the Raspberry Pi version of Mathematica. A slight change gets you the result:

SetOptions[EvaluationNotebook[],"ShowCodeAssist"->False]

This is particularly helpful on the RPi since the code assist links attempt to find the nonexistent documentation. [The RPi does not ship with documentation and users must go to the web for references.)

One can also use the menu bar. Go to Edit ▶ Preferences... and under the Interface tab one can uncheck "Enable floating elements ..."

Alternatively, one can increase the delay to a number that is big enough to prevent an unwanted pop up.