My next memorable encounter with such a story was Ray Bradbury's "The Sound of Thunder", which involved a leisure company that offered safaris to the past. One could travel back in time and kill a dinosaur. But there were strict rules so that the time stream would not be altered in any significant way. These rules are of course, broken.
Both stories showcase two very different approaches to time travel. In one approach, all events along the time stream are fixed. In the other, the slightest change in the past can result in wild deviations in the future.
There are all sorts of fancy terms for theories which fall into either category (Many Worlds Interpretation being among them). Fancy terms and theories aside, when I wanted to incorporate time travel into my campaign world, I had to take a stance.
I decided that for pure logistical reasons, I didn't want my players traveling into the past and re-writing the history of my world. It is hard enough to design a single campaign world. Creating endless variations of that world based on the whims of players hopping through time has always seemed to me to be far too much work. Instead, I settled on the idea that the past, as well as the future, are fixed. One can travel through time, but they can not re-write it.
What then, becomes the point of time travel adventures?
My approach to time travel in my campaigns has been convoluted, but resulted in many fun adventures. The basic premise behind time travel is that you may find that the things you know about the past or future are simply wrong, or that you yourself were an instrument in shaping things the way they are. Most events are malleable to some extent... as long as your excursion through time results in people BELIEVING the same things they've always believed, actual interpretation of how those beliefs came to be are an emergent result of game play.
For example, in the case of someone trying to stop the assassination of Lincoln, they may find that someone else actually committed the act and framed John Wilkes Booth. Or that Lincoln's death was faked, and it was a double that was killed. Or any number of possible events that have the end result in the belief that Lincoln was killed at the Ford Theater by Booth on April 14, 1865.
The thing to consider is that according to game world rules, the reality encountered by the players is the ONLY reality... it was always the only reality. They did not change the past through time travel. They merely discovered the truth of it.
I will give a concrete example of one such adventure I ran. The Lord of Time (who I refer to as Darkstar, Archon of Time in my current campaign) recruited a certain gnomish thief for a mission. It seems that the Dwarven city of Stonehaven had fallen to an evil force. Within the stronghold is a Dwarven artifact. If the evil forces get ahold of this artifact, they will not only subdue the Dwarves, but control them as a force. The gnome must enter the Dwarven city, find the artifact, and steal it.
Now.. the problem is that the city has already fallen, and Darkstar doesn't know if the evil forces have gotten their hands on the artifact yet. He does know that prior to the invasion, the artifact was safe in the vaults of the Dwarves. So... he sends the gnome back in time, just prior to the invasion. The gnome can't simply go snooping around the vaults, nor can he ask for the hammer. He must wait for the invasion and the following chaos to ensue in order to be able to freely explore. And so, he actually becomes part of the futile defense of the city. He later finds the artifact. Once he has it in his hands, his "recall" spell is triggered, and he is re-united with Darkstar.
Now... something interesting happened during this adventure. He found himself in a battle which the Dwarves were destined to lose, because it had already happened. While his actions could have an affect to some extent, there was a limit to the affect. He was in what many players would consider a "railroad".
Personally, I don't concern myself with such terms. I know how I want to use time travel, and how I don't want to use it. The success of the player's mission was not guaranteed. He found there were things he could affect, and things he couldn't. He recognized these quickly, and rather than complaining about it, switched strategy. He used his wits to convince the Dwarven king to move the artifact, and while it was in transit, he had his opportunity to steal it. All in all, it was quite a memorable adventure. One of the fun things about it was being able to put a player character in the middle of a battle, but be unconcerned with the overall result of it. He knew the battle was lost before he ever started. He still had many opportunities to shine, helping individuals who otherwise might have been "collateral damage".
Running such adventures is challenging. As in Back to the Future 2, people and artifacts can wind up being in two places as the same time. Time travelers can potentially meet themselves. One must keep an eye on the development of Djinn artifacts.
From a lecture by Princton professor Richard Gott:
Self consistent time travel stories have some interesting features. We
introduced the concept of a "Djinn" - a particle whose world line is like a hula hoop - a circle with no ends (the name was introduced by Igor Novikov). An example was given with the 1980s movie "Somewhere in Time", (in which a pocket watch that was given to the protagonist by an old lady is brought back in time and given to the younger version of this lady, who in turn grows old to give it to the protagonist - thus this pocket watch, which has never been near a watch factory, is a "djinn").There are numerous other challenges in running time travel adventures. Particularly ones in which time is self consistent. However, they can be very rewarding, and quite memorable for all involved.