Thus, every time travel jump into the past depicted in the Back to the Future saga "destroys" a current timeline and "creates" a new one, although Doc Brown often uses the phrase "erased from existence" to describe the deleterious effects of this process/
If time travel was possible
If you could travel back in time, you would take some of the ambient radiation in the universe with you. And the universe would then have ever so slightly more energy than it did before you went back in time. But of course this would be an infinite feedback loop creating infinite energy in the universe.
So umm... I would go see some Fischer-Spassky, but I would destroy the universe in doing so.
I would want to go back to 1574 to the first international chess tournament held by King Philip II in the Royal Court of Spain, and watch Leonard di Cutri defeat the famous Ruy Lopez.
I'd wear something distinctive to prove I was there, like maybe an orange vest with striped sleeves and skirt, and maybe some white pantaloons.
That's a tough question.
In a vacuum, I'd say Fischer-Spassky. But that happened not so far ago. New York 1924 must have been something. That Morphy tour in 1958-59 too.
Alekhine-Euwe in 1935. Just to have the opportunity to get a few drinks with a legend... 
I'd like to go back to Sept.4, 1945 New York, where Reuben Fine gave his 4 board blindfold rapid transit simul. Fine played 4 boards at 10 sec./move. His opponents could think until he reached their board, giving them essentialy time odds of 30 sec./move to his 10 secs./move. Fine won all four games. Board four was Robert Byrne.
I would probably travel forward in time to a match a couple hundred years in the future. While there, I would take diligent mental notes on all technologies, ideas, and events that have surfaced since the current time. I also might look up some old sports scores. Then I would come back to present day and become a famous inventer and make millions between my "gambling" and new technologies.
Oh, and time is philosophically weird... I'm not even convinced we're traveling through it... the lack of a "nowness" in our memories almost suggests that they might not have been moments experienced, and only "now" is real, but due to our fake memories, we believe that time is passing.
If time travel is possible, we probably haven't reached that point in time yet.
From what I understand from others, time travel into the past is theoritically possible, but only to the point in the past where they have built the time travel machine.
THat is what I mean. You couldn't fly until they built the first airplane. We haven't reached the point where we have the means to time travel yet.
The airplane does not violate any universal laws. A time machine would and therefore will not be built unless new laws are discovered which will permit it, I think.
If time travel is possible, we probably haven't reached that point in time yet.
From what I understand from others, time travel into the past is theoritically possible, but only to the point in the past where they have built the time travel machine.
Probably not. The universe is entropic.
If time traver were possible, we know that it would only be one-way into the future because nobody from the future is popping up on the landscape.
Also, life and the ability of organisms to grow, adapt, evolve, and become more organized indicates entropy and the deterioration of matter into chaos is not universal.
To answer the original question, I would like to shake hands with Emanuel Lasker and have a nice chat with him, preferably not about chess, but about personalities and fighting spirit...
But speaking about time travel : assume you are born on a planet in a far solar system and it would be possible to watch and study our earth by means of a very strong telescope, than you could see "old" light.
In the constellation Taurus are planets some 6o lightyears away from us.
Creatures who, from there, on this moment, watch the earth by those means, now see (literally) the invasion in France at the end of the second world war.
Compare your attending fireworks, the sound takes some time to reach you, but so does the light.
By the way : the speed of light : in one second seven times around the earth, a bit faster than my bullet and blitz chess playing...
I invite readers to comment on this idea of time travel and please add more insight !
I'd send Carissa Yip back to the days of Morphy just so I could see the look on his face when a little girl defeats him 
I'd also go to the future, but not so far into the future where gene therapy is universally banned, to China (or wherever regulations are least) to have extra color cones inserted into my genes so I can see far more colors (primary or otherwise). Or, I could try redefining color-blindness to include nearly the entire human race to open a loophole to allow such operations in the West. We have the technology today to do so but it isn't widespread and needs to be done before ethicists get their dirty mitts trying to ban such:
http://www.npr.org/templates/story/story.php?storyId=112897277
If time travel is possible, we probably haven't reached that point in time yet.
From what I understand from others, time travel into the past is theoritically possible, but only to the point in the past where they have built the time travel machine.
THat is what I mean. You couldn't fly until they built the first airplane. We haven't reached the point where we have the means to time travel yet.
The airplane does not violate any universal laws. A time machine would and therefore will not be built unless new laws are discovered which will permit it, I think.
Time travel does not violate 'univerasal laws" (whatever they are).
http://gizmodo.com/yes-time-travel-is-possible-heres-how-1654958816
Time has an 'arrow' and the arrow points in one direction; forward.
Examples of universal law would be the law of gravitation or the second law of thermodynamics and the speed of light and etc.
if time travel was available I might surpress Ben 10 from existence. Or at least try. but then there was no cause for me to go there so goodness knows what would happen.
If time travel is possible I believe it would be as a completely undetectable phantom as it does in Harry Potter and the Chamber of Secrets, unable to do anything.
If time travel is possible, we probably haven't reached that point in time yet.
From what I understand from others, time travel into the past is theoritically possible, but only to the point in the past where they have built the time travel machine.
Travel into the past is not possible. The Second Law of Thermo prevents it. I think. Right? I mean you can't uncrack the egg.