I have a program which saves a little .txt file with a highscore in it:
// Create a file to write to.
string createHighscore = _higscore + Environment.NewL
Something I have not yet seen mentioned is storing the high score on an online leader board. Obviously this solution requires a lot more development, but since you are talking about a game, you could probably make use of a third party provider like Steam, Origin, Uplay, ... This has the added advantage of leader boards not just being for your machine.