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.
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.