mouth-breather n. a stupid person; a moron, dolt, imbecile. Related: English, Derogatory, Slang 
 Editorial Note: The original definition of mouth-breather referred to a person that, due to medical problems (usually with the sinuses or nose), was forced to breath via the mouth. This leaves the jaw hanging open at most times, which has a tendency to make a person look dopey or spacey. 
 http://www.doubletongued.org/index.php/dictionary/mouth_breather/ 

 Since 'mouthbreather' redirects to this page, the connotation should be mentioned.