I will preface this by saying that someone else may have (in fact, probably has) thought of this before I did. The concept of a multiverse is certainly not mine, but if someone else has thought of its applications to time travel I assure you that I did so independently of them.
Assume that there is such a thing as the multiverse, the set of all possible states of the universe. Every time an event occurs with a random outcome, there exists for each possibility a universe in which that possibility is the one that occurred. Thus, when performing the famous double-slit experiment, there exists a universe in which the photon passes through the first slit, a universe in which the photon passes through the second slit, a universe in which the photon strikes the surface between the two slits, a universe in which the photon strikes a different spot on the surface between the two slits, a universe in which the photon fails to fire at all due to a power fluctuation, etc.
Now, let's consider two specific universes within this multiverse: universe Alpha and universe Beta. We will be looking at three points in time within each of these universes: moment 1, moment 2, and moment 3. Both of these universes contain an inventor named Joe. At moment 1 in universe Alpha (moment 1A), the Joe of universe Alpha (Joe-A) creates a time machine. At moment 2A, there is only one Joe present and he is still alive; this may seem inconsequential now, but its relevance will become apparent. At moment 3A, Joe-A uses the time machine to travel back to moment 2 and meet the Joe that he finds there. According to a common interpretation of time travel, Joe-A meets himself at moment 2A. However, we have already seen that there is only one Joe at moment 2A. Either there is one Joe at moment 2A, or there are two; both cannot be true. Because we already know from previous experience as absolute fact that there was a only one Joe at moment 2A, it must be true that we are not looking at moment 2A; we are now looking at moment 2B, and Joe-A has met Joe-B.
Now suppose that Joe-A kills Joe-B at moment 2B. When moment 3B arrives, the deceased Joe-B is no longer able to use his time machine to go back and kill himself. Had this scenario been played out on a single timeline in a single universe, causality would be violated by a classic temporal paradox. However, the existence of the multiverse means that both possibilities (that Joe is alive and that Joe is dead) can exist simultaneously.
In the course of looking up a few terms while typing this, I came across this, which shows that this is not, in fact, an original idea. Alas. I'll post it anyway, because it's still interesting and because I spent so much time on it.