I will go with 2.

It would create a new "dimension". It all goes in theory of that with every decision you make a new "dimension" takes place and theres a dimension for every possibility. With that in mind, i dont think time travel is as simple as traveling in just the time axis, wich is why its pretty much considered impossible. If it was possible, i would expect someone from the future would have come visit us already.
Alternatively, if it was possible with the multiple dimension theory, i guess that a new dimension would be created and future self would be stranded in the past if he only traveled in the time axis (he could travel to the future of the dimension he just changed). He wouldnt be able to return because his interference destroid or deviated the position of his dimension in the spectrum. Without travel in the "dimension" axis i would think it would be impossible for him to go back.

Wow, interesting replies and ideas... I think it all boils down to ones beliefs about what time is and how it works.

I personally believe time as we know it is a straight line and obviously goes only forwards. I don't see time as something that revolves around humans but vice versa. Tomorrow is going to always be tomorrow, however the things we do and who we are may change tomorrow. I don't think a split timeline is something that could happen since that would imply that time revolves around actions of each individual.

With that in mind, I think that if time machine was invented in a persons lifetime who lost a leg in the past, that person would have to put the effort to travel back and stop themselves from losing a leg. Just thinking about doing it will not get his leg back. The moment he travels back and does enough to stop themselves in the past from losing a leg, he disappear from the past and never exist in the form and with memories he traveled back with. Puff! Gone!

So I guess option 1 for me...

Different time lines is the key.

You wouldn't lose your leg and then that person's time line would shift allowing for all sorts of new things.
The you that went back in time would just live along in that same event.. probably richer as you should be smart enough to bring something back with you to use to gain financial superiority.

Finally total chaos as so many people would be coming back that shit would get all screwed up and while you fixed yourself from that one leg tragedy you have no clue what else is now going to happen. Really you just now have two selves living through some crazy shit.

Think about it though. How would it go poof? The future you is a collection of atoms. Matter doesnt just disappear, it gets transformed.

So where would the matter go? Your theory assumes just the time axis, so in that regard i guess that is normal to assume, but i dont think the person would go poof, theres no plausable reason for that to happen. The timeline he came from doesnt cease to exist, it ceases to be acessable if you understand what i mean. That future exists because without it the new restored future couldnt exist. That proves that the old future existed. It cant just disappear, its just lost. The you from the future that came from the past doesnt have the means to go back to the old timeline but he is on the present one. I dont see why he would go poof.

A good representation of it in the timeline would be a straw with a loop. The timeline goes in front but circles around and back to the starting point of the loop. The loop segment is no longer on the straight line to the timeline but it existed and it is there, just not in the straight line. Actually the storyline on Chrono Cross delves into this aswell because of the events on chrono trigger. Its an interesting subject.

It depends on your model of time itself. Time could be merely the way that we measure change in the universe, or it could be a fundamental part of its fabric. In the former case, option 2 would be the most likely situation. In the latter case, one would assume that some form of self-correction would have to occur in order to "stabilise" the system... but that could take one of a variety of forms.

The simplest form would in that case be that the future self would change due to the changes in the timeline, and would be seen to travel back in time purely to maintain the timeline - that is, despite not losing the leg, you would remember being visited by your future self and that doing so saved your leg. So you would travel back in time to keep yourself from losing your leg. You could argue that this model was applied, for instance, in Bill & Ted's Excellent Adventure, as well as that Star Trek TNG episode where we see the first time (temporally) that Picard meets Guynan and Data loses his head for a few millennia.

Of course, such a "simple" version only works when there's a logic that can maintain the immediate effects.

But it's likely that the real answer is that time travel to the past isn't possible, due to inherent contradiction. That, or the universe is completely deterministic, so that time travel may happen without creating any sort of loop, in which case any time travel involving the past has already happened. One last possibility is that there's some sort of force that prevents stable loops in time - one that would, for instance, prevent you from killing your grandfather as a child.

who knows, you might be caught in an infinite time loop and your past self would be annoyed by you arriving every 20 minutes to tell him not to go on that boat, while the past slowly fills with time copies of your future self until you are hunted by the government who wants to kill you to prevent you from travelling back in time

future u would disappear once past you avoided the boat, or future you's leg would comeback after past you avoided the boat.

i said that to a long time friend who believes in god. i'm sure you know wht happened.

You can't go back in time to "save yourself"... That's the thing.

You imagine the issue as if it was like this:

- You have an injury in 2012. 

- Years go on, and time travel finally gets possible in 2025.

- You go back in time to the year 2012.

- You save yourself from getting injured.

The problem with this is that when you first experience 2012, if your 2025 self travelled back in time to get to that very 2012 you're currently in, he is there all along when you first experience it. 

I personally much prefer the terminator ideology.

As much as I'm a sucker for time traveling movies, I'm not really a fan of stuff changing in the future based on actions you take in the past, or people disappearing. I mostly like the parallel universe theory/explanation to everything.

So in this case. The world you lost your leg in will continue on with you out of it. You are then in a parallel universe stuck with another you who avoids losing their leg, and life goes on.