For what it's worth, here's a fascinating story, told by Lama Govinda in his book "The Way of the White Clouds," of a child who recalled vivid details of previous life - and Govinda met the child about 4 years after the incident took place.
A 4 year old child in 1930s Burma was going with his family to a local fair. The family was completely illiterate without any formal education.
At the fair, someone came and offered some candy to the child and his 6 year old brother. The older brother took it eagerly but the younger child - who suddenly felt a host of memories flooding into his mind - asked the father to raise him onto the father's shoulders.
The child, to the amazement of the crowd, proceeded to give an erudite Buddhist sermon on the values of gratitude and self offering. When he concluded, he said to his father, "Take me to my monastery."
The father of course had no idea what his son was talking about, and had never visited any Buddhist monasteries.
The child gave precise directions to the monastery, which was over an hour from where they lived. When they arrived, the child said to the monk who greeted them, "Don't you recognize me? I was the abbot of this monastery."
They went through the standard tests for remembrance of past lives. The child LED THEM through the monastery, describing (before he reached them) the contents and purpose of each room. He led them finally to the room where he, as abbot, had lived.
They arranged certain of the abbot's possessions mixing them with others. The child easily identified those which belonged to the abbot. He also read long passages from various Buddhist scriptures written in the ancient language of Pali. Note that the child would not have been exposed to Pali at any time in the 4 years he was alive, and remember again everyone in his family was illiterate.
The child then asked to speak with the monk who had been there longest. They went out on a boat where nobody else could see or hear them, and the child told the monk what his name had been before he entered the monastery - since nobody alive would have known the monk at that time, it was clear that this child was remembering an actual incident.
Now, I know some people who accept parapsychology but not past lives. They say "well the child could have tuned into the morphogenetic field or universal mind to access those memories."
Which doesn't explain how he was able to improvise an erudite Buddhist sermon, or how he was able to read Pali. And why are telepathic abilities easy to understand but past lives not?
Because no matter how flexible our minds are, we still cling to the belief that "I" am this body. So it seems impossible to imagine consciousness and memories associated with a different body.
The thing is, if you even just take a moment to carefully examine your experience, you'll notice that what you call "matter" or "body" is a collection of sensations in awareness. And if you continue examining this way, you'll discover that you as infinite boundless awareness were never born, so you never can be reborn.
Rebirth is like having a dream about say, being an engineer, then waking up to your waking identity as say, a painter, and then the next night resuming the dream about being an engineer.
Only in rebirth, it's not a series of dreams tied together in association with what we call a "body" but rather, the dreams are tied together in relation to the same Infinite Awareness which is the only true SUBSTANCE there is.