We have long discussions about time travel. Some of our group have vary concrete positions on the topic (i.e. "It's impossible!" to "It creates an alternate universe" and so on).
I'm going to keep it to how I would handle it in an RPG.
Time Travel, for me, all hinges on the specific moment in time you originate from.
I will not allow you to go BACK and time and change anything. You can go back in time, but you can change nothing. No matter what you do, or even possibly
because of what you do, the same events will occur. You can go back and see what happened though. Additionally, you need to return to the exact moment you traveled back in time from. Seems like an arbitrary rule, but it stops things from spinning out of control. You can explain it to the players/character as something that MUST be obeyed or they will return to an alternate reality or, if you want to be even more hard and fast about it, they'll simply cease to exist due to messing with the 'space-time continuum'. So, the "prime directive" if the players were given specific instructions from a time traveler would be "Observe only. Do not try to alter the outcome or you will only find yourself an accomplice to the destined result and always return back to the exact moment you traveled back in time from or the results will be catastrophic." For example, if you go back to try and prevent a death your actions will, at best, be for naught and, at worst, might actually implicate you (I know, that's potentially changing things... but I warned the players not to mess with it!).
This stops things like "Crap! Bob just died! Quick! Travel back in time and tell him to dodge that round!" If you allow the alteration of the past you are opening up a can of worms that you will likely regret as the GM. Just don't do it. Madness lies that way!
Now, you can play with things a little. I'm going to use two very specific examples in how you can actually use backwards time travel to your own benefit (aside from just seeing what happened).
1. You are told to meet someone somewhere in a place not of your choosing. They are already there and you must go now. Let's say you have a favorite gun, but they tell you no weapons and (for arguments sake) set it up so there's just NO WAY you'll be able to sneak any gun, let alone that one, in. So... you go back in time, go there when no one is there, plant one or more weapons or grenades or cameras or whatever the heck you want there. You then travel back forward in time and show up, on time, obeying all the rules. You have not altered your past in any way. This is how players can use backward time travel to their advantage. (Yes, someone might see you do it or randomly find the things you hid, but you get the basic premise).
2. Get a little more creative with it if you want to allow it: You want to do something for yourself based on events that have already occurred, but due to the nature of time cannot alter your current reality in any way. Let's say I wish I'd invested in Microsoft when they were being run out of Bill Gates garage (or wherever he started). I can't just go back in time, invest, then come back already a bazillionaire. That would be changing my current reality. You need to have to do something
after you return that accomplishes this. So, let's say I go back in time, invest money in Microsoft, then come back, go to that investment firm (or whatever) and act as if I'd known about that account all along. I haven't changed my past. I was still just as rich or poor up to that point. Any notices, emails, phone calls or anything else related to it don't reach you for one reason or another over the years.
So, forward travel. That is a completely different ball game. So long as you are traveling from the past to the future and back again you will be able to change future events because they have not happened yet. So, you need to know if someone planning on invading your country? You zap forward, see what happened, zap back, and take whatever steps (if any) are needed.
The first reason I do things this way is because it doesn't create a nightmare for the GM. You really don't want players messing with the past unless you want to hand them the ability to completely wreck havoc within your campaign. But allowing them to travel forward and gathering information can help you 'encourage' them along certain paths or, at the very least, not unravel everything you've done.