Aye - time travel is the proverbial can of worms.
Four possible suggestions:
a) If you are able to have a sage tell the adventurers that there are an infinate number of parrallel universes where different choices/actions are playing out, then when they travel through time they are
really traveling to a specific parallel universe. They are changing the time stream on that alternate universe where the changes are happening. THus, when they return, they will still have the current "fate" of the world but the other one is the one that has changed.
(Yes, that's a bit weak and may not be satisfying to the players because "thier" world is still in the same previous state)
b) time travel -- but always to the future to chance future events written in fate
c) time travel -- but always to some remote area/something or else somehwere where the changes would be minor. (this was sort of how Quantum Leap did it (an old show in the US for those not familiar) Sam was always changing generally "minor" things. Helping a specific single person, etc. There were a couple times that he interacted with his parents or sister but no one really believed that he was from the future. This of course worked because the time travel was back far enough that there wasn't a chance of meeting himself.
d) Have a GOOD event in history (example: the kingdom won a war against the orc invaders - something large enough for it to make a difference and yet the specifics are unknown enough for just about anything to be the reason - i.e. could be any number of deciding battles that turned the tide in the war example given) - some event the PCs already know of or is considered common knowledge (i.e. "the kingdom won that war against the orc hordes"). Unexpectedly, the PCs are asked (or told or end up) in the past at said event. They know in thier history that the event ended good (kingdom won). But while there in the past they find out their team (the kingdom) is about to really lose. Once they make the connection that they can not let the bad side (orcs) win, they will/may help. In the end, presuming the PCs were successful, the event ends up good. Thus, everything is how they remember it and the world continues as they know it to. You remove the possibility of paradox because you essentially give the background that they were successful and then they go back and find it's going poorly making it "good" thus _making_ the history that they and everyone knows/remembers.
(this last one may be the most satisfying of the time travel options i list here but it requires that the DM ensures that the PCs get themselves involved to fix things*)
*Even if the PCs don't win, maybe they could go back to the present. See all that is wrong (they remember the other history because they were traveling through time when the world "reset"). Maybe have an adventure or two in this "alternate" world. Then go back in time again to try and correct what they were unable to fix the first time.
Basically: Rather than stopping a bad thing from happening, they are going back to ensure a good thing (that they remember) does happen.
I'm really bad at explaining things like this so sorry if this sounds unclear...
I did do #d before. When the players saw that the "good guys" were losing, they kept assuming that they somehow disrupted the event (thus furthering their desire to make things right). It was only towards the end were they able to realize that the event was not suddenly being lost because they came (it would have lost in the original timeline if they didn't come back) it was won because they came....
editing: adding some clarification here and there to my post