"Watergate" is a general term used to describe a complex web of political scandals between 1972 and 1974. The word specifically refers to the Watergate Hotel in Washington D.C. This scandal eventually led to the resignation of Richard Nixon as the US President.
http://www.watergate.info/
Since then, it has become fashionable to name scandals with "gate".
Jenson Button, a current Formula One driver, was embroiled not once, but twice in two sordid affairs where he attempted to get out of his contract to go to another team. This most certainly tarnished the credibility and reputation of Mr Button, and obviously, is where the term "Buttongate" comes from.