Each tournament has its rules, but what I was taught as a child when I played was that the agreement of the players was the end of the game; if you weren't checkmated, it was treated as though you resigned because you thought the position was a lost position. Shake on it, and the game is decided.
As the winning player, it was considered unsportsmanlike to not point out the available move, but not obligatory. The winner may not notice the move itself! I remember one game where castling was the difference between being mated and winning the game, but it never occurred to either player that, that late in the game, someone might not have moved either their king or rook. I also heard of one game which would have been won by an en-passent (but I never did confirm that it occurred).
In the end, it really depends on the situation. If there's more important things than winning (like having fun and learning), not pointing it out is bad form. If winning is all there is (which might happen in some master level play for large money), then... well... hopefully you don't make a mistake like this. Usually the mistake at the masters level is resigning from a winning position, and they usually don't need their opponent to tell them about the mistake later -- all of their friends and their chess computers will make sure they know afterwards.