Every major religion has a creation myth that has elements of gods creating human beings on Earth. Several religions also believe that once a person dies, their spirit will be reincarnated into another person (or form).
The ancient Egyptians had a complex view of reincarnation. Their belief system is founded on two gods coming to Earth to begat mankind. The subsequent Pharaohs were believed to be the reincarnated souls of those original gods. Since they were gods, Pharaohs ruled with impunity.
But the incarnate god was not reserved just for royalty. The Egyptians believed that when a person died, his "ba," the spirit associated with one's character and personality, leaves the body to find a new vessel in which to be reborn. The souls of the departed continue to return to new bodies for an infinite cycle.
There have been several research papers on the subject. Scientists interviewed various people from different parts of the globe who claimed to have remembered clear details of their past lives. Scientists then would take this information and try to independently verify the recalled facts. In several instances, researchers concluded that the interviewees remembered things that they could have not known (personal information, names of relatives, phone numbers, houses, etc) that were not accessible to them in the present time.
There has always been a puzzle when reproduction happens in people. When the egg and sperm fuse, historically it was said there is a "spark of life," some form of energy which gives rise to fertility to the newborn. Theorists think that spark of energy may be a soul that the fuels the rebirth of a spirit.
On the other extreme, in the realm of B-movie sci-fi, science knows of all the elements of a human body, its chemical composition and structure. In theory, what is missing from the base elements is a form of electrical current that makes the human organs (including brain) function. In Frankenstein, the mad scientist uses lightning bolts to jump start "life" in a corpse. This "re-animation" is different than reincarnation since the former tries to re-use the old vessel to bring back a person's life.
It is not as far fetched as one would assume since emergency room personnel routinely revive cardiac arrest patients with electric stimulation. But in the re-animation world, it is assumed that the brain functions as a storage device for all memories, personality, speech, etc like a turned off hard drive. Turning the brain back on would revive that person's personality.
But the Egyptian view would say no. The dead person's character and personality is not located in the brain but in the spirit (or soul) of the individual. And once the person dies, their soul leaves the body so re-animation will not work.
In the Egyptian dead scrolls, it is said that the deceased spirits have to journey through the underworld to be judged before being reborn. And since one spirit can be reborn more than once, the journey could be fraught with danger.
In LOST, the island could be a representative underworld where souls travel to begin their journey to the after life. This would explain why certain characters, Mikhail Bakunin, could apparently die over and over again on the island. It could also explain how Desmond survived the Swan station implosion to be found naked wandering around the jungle (symbolic "reborn.")
One of the story principles in the series was giving the characters "a second opportunity" in life. Reincarnation would be a means to give a person (especially a tortured soul like Locke) a new beginning, a new life.