Players are expected to remember their own triggered abilities; intentionally ignoring one is Cheating. Players are not required to point out the existence of triggered abilities that they do not control, though they may do so if they wish.
Triggered abilities are considered to be forgotten by their controller once they have taken an action past the point where the triggered ability would have an observable impact on the game.
Triggers happen all the time in a game of Magic and it can be difficult enough for a player to remember their own triggers, let alone opponents’ triggers. We don’t penalize players for not pointing out their opponent’s forgotten triggers, but it is cheating for a player to intentionally ignore their own triggers. Cheating is dealt with according to the IPG or JAR, as appropriate. If a player notices that their opponent forgot a trigger, they may point it out.
Triggered abilities that are forgotten are not considered to have gone onto the stack. How forgotten triggered abilities are subsequently handled is defined by the Rules Enforcement Level of the tournament.
Our good friends at the Annotated IPG project have a lot to say about missed triggers. Let’s let them take it.