We will take a look at the two general theories of time here. There are many theories and when you get down to the nitty-gritty you have to take into consideration how motion and gravity affects time, how cosmic time works, and how they all come together. From Newton to Einstein to Hawking; from World Lines to Person World Lines; it can get pretty complicated and contains too much information to digest in one article. We will just construct a layman's view. After all, we are trying to find ideas for your game, not trying to build a time machine out of dice, paper, bags of Dorito's, and cans of Mountain Dew.
Circular (Linear) Theory of Time
This is the most widely used theory in plotlines. Basically, when you travel back in time; what you change will affect the future you came from. You stop someone from getting hit by a car and dying, the person will continue living when you get back (Maybe that is, it does not mean that person will not die of a heart attack the next day of course). The trick to this is how FAR you go back in time. The closer the event was from the point of the "time jump" the less time ripple effect will occur for the time traveler(s).
Parallel (Nonlinear) Theory of Time
The Parallel theory states that each timeline exists in dimensions. Basically, for every cause there is an infinite amount of possibilities which result. So if our time traveler(s) travel back in time and changes something, the new timeline is created in another dimension. So when the time traveler returns to the point of the "time jump", nothing has changed for them. This adds another factor to your game. Dimension travel. So in order to live in the dimension that was changed, they must "Jump" into that dimension. That leads to another factor. Now there exists, in the dimension, another existence of the time traveler(s).
The ultimate sin in time travel. This must be avoided in gaming at all cost or you will end up with a mess of a campaign and perplexed players. A paradox can happen easily in time travel. When you get into a paradox, you enter an illogical continual loop.
For the Circular Theory, this can be caused for instance, if you were to travel back in time, did something to kill your great grandfather, thus you would have never been born, thus you would have never time traveled back in time to kill your great grandfather in the first place but you did travel in time, so you did not kill your great grandfather, so he lived so the action you took did not kill your grandfather... Add infinity.
There are two concepts to help prevent a paradox. The first is simply, "Everything that has happened, that will happen, MUST happen". If the traveler jumps back into time and kills his great grandfather, he would encounter diviation and mishaps that prevent him from killing his grandfather.
The second possibility is simply to use the Parallel Theory. Change the future? Get a new quantum universe!