Ke2! is a dubious move. An early 'joke' idea of this move is to prepare for an early endgame by developing the king. However, the problems with 2. Ke2?! are that the King move prevents castling to protect the King, endangers the King, ignores development and the center, and blocks the Queen and Bishop, which are the two pieces that are free after 1. e4. All that being said, it can be used as a surprise to unseat Black. Due to the dubiousness of the move, it can be used as a form of a handicap system.
Sometimes, games are played that begin with the Bongcloud Attack in which the players try to move the king to the opposite side of the board rather than achieve a checkmate.