One of my favourite game systems is the Primeval RPG, and damaging the timestream is a possible thing that happened all the time it seems in the tv series, sometimes more subtlely than others. :)
So I figured today, seeing as how I'm also running a Primeval RPG Play by Post (PbP) game, PRIMEVAL: Tales of the Anomalies, I would post up here how the game handles this problem, called Temporal Damage, though not all the details.
As the rulebook points out...
As Nick Cutter learned tragically, time can be changed. Go through an Anomaly and alter something in the past, and that change can ripple through reality and shunt you onto a new timeline. It may look very like the world you came from. The differences may be so small as to be insignificant, but make no mistake - changing timelines makes you a stranger in a strange land. Change time, and you wash away one version of the universe and replace it with another - and there's no way to know for sure what will be changed by your actions. Even trivial actions can affect the timeline. It's the butterfly effect - step on an insect in the Jurassic, and you may have just erased the world you knew.
Fortunately, time's got a certain amount of resilience... or inertia. It can cope with minor damage to the past without triggering a change in the timeline. The temporal inertia is bigger the farther back you go. If you travel back two billion years ago, then any changes you make there are likely to be irrelevant compared to the vast weight of time between then and now - it's like trying to change the course of a river by kicking the mountain it flows down. However, if you make a change in, say, 1900, it's going to be very easy to unmake the world you know and replace it with somthing else.
Temporal Damage is a way of measuring damage to the timeline. If the player charactrs aren't careful when dealing with the Anomalies, they'll accrue Temporal Damage points. This doesn't work like normal damage. Instead of applying to one's character Attributes, it's applied to... well, all of reality.
Here's how it works. If you do something that might alter history, then the Temporal Damage score rises. If you undo whatever you changed, then points are taken away from the Temporal Damage score. You want to keep Temporal Damage as low as possible.
Sources of Temporal Damage
Killing or failing to return Time Shifted creatures.
Travelling to the past.
Leaving someone or something behind in the past.
Keeping future technology.
Deliberately altering the past.
So... 'nuff said. :)
Oh, and for the record, there are a total of two (2) spots left in the Play by Post game, for those that might be interested. :)