Look at Bill and Ted's excellent adventure. If nothing else, it proves only two burn-outs can travel through time successfully without paradox. In the beginning of the movie their future selves show up, and a discussion takes place. In the end of the movie, the boys see their past selves and have a discussion different from the original one. Their past selves will not have the same memories as the present selves, and so when they travel through time a different conversation will take place with the more past selves, and so on. Because the conversation was accidental, it has no real consequence except that every pair of bill and ted will have a different memory about that meeting.
However, let's say you proclaim that if you ever get to travel through time, you will come back to the moment of proclaimation to cut off your own left pinky finger. Just then you come in, a bit older but not really noticably, cut off your own left pinky finger and disappear. You now know that you get to time travel in a few years, and you have the proof. Problem is, you want your pinky back, so when you get your chance in a few years, you go back, do not cut off your pinky, but rather give yourself an assurance that it's real. Well, you may be satisfied, but your past self needs more proof, so his time around he does something more drastic, like inflict a scar across your face. The more past self gets a chance and doesn't do a scar across the face but rather he removes your right buttock cheek. The more more past self wants his cheek back, and thus cuts off the big toe. The more more more past self wants his toe, and so gives vital financhial secrets to the next one in line. The more more more more past self discovers money is the root of all evil, and commits suicide before he can travel back in time. You now cease to exist because your past self commited suicide. Even though you did not interact with him, another past self of yours did when he (or she) traveled back in time after you already had. Because of the infinite variation occurs because no two occurances will ever be the same, you are doomed out of existance because every single possiblity will play out, eventually leading to suicide or murder of the past self. Problem is, if the more more more more past self never travels through time, because he (or she) commited suicide, how will the more more more more more past self get the financhial info that leds to suicide? That one won't, and therefore will travel back in time... but that self already died in the future, even if it is your past. Because this seminal event of time travel will continue to vary, it's impossible for it to end, but it's impossible for it not to end. Therefore, not only do you cease to exist due to paradox, but so does everyone else because the universe's fundamental laws are torn asunder.
Note, that this does not happen if you visit the future, since your past selves will have no fore knowledge of events, they will always react the same way as you do, because they are you. So no matter how many past selves travel to the future, their experiance will always be the same. This also kinda goes along with the prevailing theory on time travel, if you will, that it can only happen in a forward motion. Take the twins example. A set of male twins just turned twenty when one of them hops on a rocket for outer space. There, he travels at near the speed of light around the earth for a time equal to him of one year and a day, thus, he lands on his birthday. He finds out that today his twin is celebrating his eightieth birthday, not his twenty-first. Because time slowed down in comparrison between the rocket twin and earth twin, one could say the rocket twin traveled forward in time. Of course, there is no traveling back with this method, and really has nothing to do with my essay since there is no flux capaciter.
Well, like I said, my biographer had a differing opinion that, while optomistic, is kinda the logic defying feat we so rarely see from the straight man. He postulated that the past is the past, and the present the present. We live in the present, and it will always be the present for us, traveling along with the flow of time (sorta like the langoliers but no monsters or creepy blind girls). If I go to the past and kill myself, my past self dies. However it has no effect on me or the people I know. I died in the past, true, but in the present I didn't die in the past. Basically, the first time around is what determines the present. You can mess with the past all you want, but as long as the present continues moving forward the past will never catch up with it. If I go back in time to the civil war and nuke all of America, then it's a nuclear wasteland. However, in the present America will be fine because it was never nuked in the past. This may sound a little confusing, cause basically there are two pasts. There's the past that happened, and the past you can change. It's like an alternate dimension, if you will, you can mess around with it, and not affect the present. So if you were so inclined, you could kidnap some beautiful women and make them become your silicon induced sex slaves, no one would miss them and you could justify to yourself they are better off this way, which of course they are not. Or you could rob and plunder gold, diamonds, or other precious commodities such as extinct animals. It would not change the present, but it would alter your future dramatically. Fortunetly, because you ripped it out of time, everyone would see it as a fantastic forgery no matter what it was. Let's say you steal the Mona Lisa. It's gone in the past, but still exists in the present, so even though yours is an original it hasn't aged the amount of time it would have if it remained in the past, thus it appears to be a fake because it is younger. You an alter the past as much you like, such as giving yourself stock tips or dating advice, but it will only alter your past self's lot in life, not your own. I like this version of time travel more than my own idea, simply because it means I can loot valuable items from the past and none be the wiser. such as poon.