A scandal involving alleged illegal acts and often a cover-up, especially by government officials.
Here are some famous examples:
Watergate - The original "-gate" scandal. It involves taped conversations documenting the Nixon administration's attempt to cover-up the investigation of the Watergate Hotel break-in which ultimately led to former U.S. Pres. Richard Nixon's resignation.
Monicagate - Named after Monica Lewinsky, who made headlines because of her sexual relationship with former U.S. President Bill Clinton.
Camillagate - Controversy arising from taped phone conversations between Prince Charles and Camilla Parker-Bowles.
Here in the Philippines, there's...
Juetenggate - Refers to the series of events leading to former Pres. Joseph Estrada's ouster after being implicated as a beneficiary of illegal gambling proceeds. (Jueteng - an illegal numbers game.)
Juetenggate 2/Gloriagate - attributed to Pres. Gloria Macapagal-Arroyo, who, has fate would have it, has had family members also implicated into allegations of recieving payola from jueteng operators. In addition, Pres. Arroyo has also been embroiled in a controversy involving taped conversations purported to be proof of cheating in the last elections.
Wikipedia: List of scandals with "-gate" suffix