Reincarnation is possible. Not the karma-driven reincarnation that Buddha would have you believe, but chemically driven reincarnation. The kind where your collection of chemicals reassemble themselves again to regain consciousness. As Sagan put it, your "star stuff" can again become self aware. It happened once, and though extremely improbable, it can happen again.
Why do I ponder such improbabilities, and if it's so improbable, why do I care? The answer is both simple and contradictory: time. I seemingly have had all the time in the world to allow my mind to wander far enough to arrive at this conclusion, yet I have very little time to do anything about it or to capitalize on my existing self-consciousness (life). I run, and lately, I have been doing a lot of it. The majority of my running happens several hours before dawn, in a pain tunnel devoid of humans, with clear views of the Universe, a few families of deer, and the occasional coyote. The perfect venue to let my mind contemplate such obscurity.
Like it or not, all organisms are just ensembles of highly organized and complex chemicals, proteins, and electrical impulses working together for a specialized purpose: life. Through millions of years, evolution has made us into the most advanced form of life ever known. When we die, it will only take fractions of frames in the cosmic calendar to reduce us back into our chemical constituents. In the process, our carbon, nitrogen, phosphorus, oxygen, and sulfur are returned to Earth. We are dirt. Worm food; to be reused or taken up by other organisms; to remain useless bits of nondescript material tucked away in a pocket of the Universe never to be touched again; to be recycled into a polyethylene plastic bottle, or in the unquantifiably slight circumstance, to have your chemicals reassemble into life. And even less likely, to return to life as
Homo Sapiens. Except this time, it is no longer you.
Herein lies the most painful and disturbing part: except for regaining consciousness, becoming self-aware, and being human, you have no notion of your previous existence. Chemicals have no memory. You owe your current existence to an infinitesimally small chance. You are you because planets aligned. Pure chance. For you to come into being again (in any form) would require overcoming equal or greater odds. Even so, assume your chemicals in all their complexity are able to reassemble into human form. Now further assume that this reassembly happens in the very next generation. You are reborn into a world which still contains your friends, loved ones, and your offspring. You potentially walk the Earth side by side with the very same people that you brought to be; though you (and they) would never know it.
No recollection. No memories of your previous life. Nothing.
Having made it this far, you should consider yourself one of the lucky ones. Perhaps if you are really lucky, your star stuff will be reborn into that plastic water bottle; leaching yourself into its contents to be ingested by another human, made part of their DNA, and passed on to their offspring (and for your sake, I hope this person isn't a total douche bag).
...but chances are that this is the only shot that you'll get. You will only live on through the memories of others, and even then, for only a generation or two. Your life is in their memories. Make them count.