To reach the game hole. To win
To meld and/or discard one's last remaining held card(s).
To achieve the points necessary to win a match.
Achieve the desired number of points in match play to win the match. There is no need to double your opponent if you will already win enough points to go out without it.
In match play: to accumulate the required points to win.
When a player is the first to play the last tile in his hand in a matching or scoring game. Also called "domino."