While it is a rather staple scenario in a lot of Sci-Fi (heck, they travelled back in time every other episode in the various Star Trek shows), time travel has never really been dealt with in the Star Wars setting (at least not as far as I've ever seen). Therefore, I found the idea of time travel in my Star Wars campaign to be intriguing—though I never 'went there' during my initial two-year run of the game.
The reason for my hesitation was the whole paradox thing. When you throw a chaotic element like player characters into a situation where they could change the course of galactic history, you should probably sit back and think things through a little while. In my overall experience with time travel, there seemed to be two main schools of thought on the subject:
1) The Star Trek Theory: Every decision creates a different parallel time-stream. Thus, you'd have an unimaginable number of different timelines all existing at the same time.
2) The Dragonlance Theory: No matter what you do, you can't change the course of history—the names and faces may change, but the end result is the same. This was likened to a river, where you might subtly alter the flow of water, but it would continue on its course nontheless.
Neither of these options sounded especially appealing to me. In option one, in fact, they often contradicted their own theory, by having people go back to 'fix' the mainstream timeline. Which made no sense with the whole parallel timeline thing, but.. whatever. I also didn't like the 'fate' element in option 2, where nothing you did mattered. So, what was a GM to do?
I had a few ideas, but it wasn't until AFTER my first time travel adventure that I finally 'locked down' my personal theory of time travel. This first adventure involved the characters raiding a remote imperial asteroid base where (according to intel) they were developing some kind of teleportation technology. What they discovered, however, was an Imperial plot to send a team back in time to stop the destruction of the first Death Star by killing Luke, Leia and the others while they were still onboard. What resulted was a behind the scenes shoot out between the characters and the imperials, even as the events of Episode IV played out. I honestly don't remember the particulars of HOW the time travel machines worked. As I recall, the time travelers used a 'pod' to teleport themselves in time and space, then had a 'return' device of some kind that would open up a door for them to return.
It was in this first adventure that several major things happened. First of all, I began to lock down my time travel theory. This was prompted largely by the fact that one of my players (Todd) put forth the idea of "Why don't we time travel to ten minutes before the Imperials left and just stop them from going?" It was a practical idea, actually—even though it would have completely thwarted the whole time-travel aspect to the adventure! For a moment, I was thrown for a loop. Luckily, the other characters quickly poo-pooed the idea (using some pseudo-science explanation of "well, since they left before us, they would have already changed the future, so...). I also think the players were looking forward to going back in time, and didn't really want to miss out on the opportunity by using the more practical approach.
Secondly, this was another showdown between Rina Nothos' team and the character's team—Rina being a major nemesis of Arianne. The final showdown on the Death Star turned into a massive brawl/melee/shootout in which Rina (shot by Arianne) was tangling with another character (Oman) when she was shot again (by Oman) and the two of them then fell into a time rift and disappeared.
Thirdly, this was the adventure where Rick Oman (the Mandalorian) got lost in time and wound up in the clone wars era—where he assumed the name of Fenn. He battled through the years, fighting in the war and afterwards (and even alongside Boba Fett on a few occasions)—but he tried to keep a relatively low profile, so as not to disturb the past TOO much. This brought him full circle to when he encountered his younger self and helped 'him' finally liberate Mandalore from Imperial oppression. How is THAT for a paradox?
By the next time I was ready to run a time travel adventure, I had things all worked out, theory-wise. How it works in my game is this: There is a main 'timeline'. It can be altered at any moment—causing it to diverge. But at most points in time, these divergences do not have any long-standing effect. In this way, it is somewhat like the Dragonlance River of Time. Oman's experience is like this. A slight change in name and face that didn't change the course of history. HOWEVER, there are specific points in time (dubbed 'nexuses' by the Imperial scientists who came up with the technology) where MAJOR changes to the timeline can be achieved. These generally coincide with major events in the galaxy—like the battle of Yavin, or the start of the Clone Wars, etc. (essentially, the points of time shown in the movies are nexuses).
This prevents the whole 'lets go back in time 10 minutes' solution—because unless 'ten minutes ago' was a time nexus, any changes made wouldn't have any major effect on the timeline (i.e. some other thing or cosmic coincidence would prevent it). This also eliminates the parallel timeline thing, which just gets quickly confusing.
My next sojourn into time travel was with Adren and her nemesis Lord Qar. In this case, the insane Sith Lord got ahold of the Imperial time-travel technology and went back in time to assume the role of Emperor (by killing Palpatine/Sidious when he was less powerful). He established a bizarre and twisted version of the Empire, based upon his own whims, turning it into a chaotic playground where he took delight in tormenting the various figures from Adren's life (her family and friends). Thus, when Adren followed him, she had to endure a nightmare tailored especially to her. She managed to defeat Qar, however (and in the process prevented him from killing the Emperor—how's that for another paradox?) and returned to her own time with an intense dislike of time travel—so much so that she subsequently broke into a high-security Republic science base and destroyed the technology that had been captured from the Vermillion crew's previous mission to the Death Star.
Alas, Adren's actions could not prevent one MORE madman from utilizing that technology (still in the hands of the Empire). Rogue ISB Agent Barezz was on a personal crusade to rid the Galaxy of Force Users and all other genetic 'freaks'. By this time, his obvious obsession and insanity had alienated him even from the Empire—thus, he had to come up with some force capable of conquering the galaxy—but also one that HE was in control of. In his research, he had stumbled upon records of the Charon (from the Otherspace Adventures).
Foolishly (in retrospect) Barezz managed to time and dimensionally travel to Otherspace. There, his 'negotiations' with the Charon quickly fell through. The bugs 'modified' him, picked his brain, and managed to cross over to the Star Wars Galaxy in force—striking prior to the Clone Wars and devastating an unready Republic. When the Character's finally managed to 'follow', they at first wound up in the nightmare future where the Charon ruled the galaxy. There, they encountered several survival/resistance groups, one lead by an elderly, but still steely Princess Leia, the other lead by an elderly but still reckless Han Solo—and both including several personages from both the Empire and Rebellion in the previous timeline. With the help of Han and Leia the party managed to repair their time-ship and made the jump back to the Clone Wars era, where they joined with a young Ben Kenobi and Anakin Skywalker and managed to thwart the Charon crossover.
This was the adventure where Lee's character (Syril Vanus) was seriously pondering killing Anakin to prevent him from becoming Darth Vader. It was touch and go for a while whether or not he would try—and the moral discussion among the players was actually pretty fun and interesting—the argument being that if he did, he might change the future, but he would also prevent Luke and Leia from even being born...and then nobody would be there to stop the Emperor.
All in all, I have GREATLY enjoyed my the various time travel adventure's we've had. I'd love to do another, but I don't want to overuse the concept (like they did in Star Trek). But with my Time Nexus theory, I feel like I have a good framework if I ever DID want to delve into the past again. Hmmm... KotOR anyone? ;)