Making them dusty.
Damn near every time travel game I've played has ended where you basically stop yourself from starting the whole plot so that none of it ever happens.
In the sense that everything you did was pointless: BlastCorps. It's a "puzzle" game about destroying everything in the way of an out of control truck carrying a world-ending nuke on it, with the goal of having it safely crash into the ocean... But it still blows up and destroys the world at the end. 😩
The first one I remember crying from (because the game itself and not just out of frustration anyway) was when Arith dies in (the original) Final Fantasy 7.
Modern games, with more sophisticated stories and actual acting tend to elicit emotional responses more than when I was a kid; though some of the epic CRPGs still hold up because they were just better written.
If I know I am going to have to make a big decision, I put on my thinking diapers.