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What are some Buddhist ininterpretations of claims of past-life memories?
There are stories of people who claim to remember their past lives. Such stories have been investigated by researchers such as Ian Stevenson and Jim Tucker.
These accounts lend themselves nicely to Jewish and Hindu understanding of transmigration of souls. How do they fit into the Buddhist understanding of rebirth?

Welcome to the site. I'd just like to mention that, you ask about "the Buddhist understanding of rebirth", but maybe different people or different traditions have different views on that subject. If there are several answers they might say different things. So far as I know, it's Tibetan Buddhism that has the strongest tradition (or which has evolved a tradition) of "reincarnation" (see e.g. Dalai Lama's Message on Reincarnation).

This statement from the Dalai Lama, linked above, would appear to provide one answer to my question:

I didn't hope to answer this question, but only to comment that there might be diverse answers even though you asked for "the" Buddhist understanding.

I've adjusted the question from 'the' to 'some' to allow for the fact that Buddhism is not monolithic.

There are stories of people who claim to remember their past lives. Such stories have been investigated by researchers such as Ian
  Stevenson and Jim Tucker.

I read Dr. Weiss's "Many Lives Many Masters" before I start learning Bhuddhism. As I re-digest the content, many questions: a) Why every turn of a rebirth the character recalled she/he a human being? For there are 6 main scopes of lifeforms. A rebirth, on account of Karma, one could be Celestial beings, Asura, Man, Animal, Ghost, Hell beings. According to Tibetan tradition, almost only a Saint could return consecutively 7 times a man. b) Why many of them claimed they were Egyptians in their past lives? Etc. I can't comment IS and JT since I've not read any of their works. I intuit theirs will be similar to Dr. Weiss's.

These accounts lend themselves nicely to Jewish and Hindu
  understanding of transmigration of souls. How do they fit into the
  Buddhist understanding of rebirth?

Therefore I would tend to acknowledge that your mentioned "Jewish and Hindu understanding of transmigration of souls" is different from the Buddhist. In Buddhist teaching, there isn't a "soul", or permanent "self" that brings along it's memories and karma etc and jumped into another body, and lives again. In Buddhist, this "living" is like fire, passing from one log to another, that's "rebirth", if one may call it. But we cannot say this fire is the same fire that burnt log A, now is burning log B, for we cannot consolidate a fire, preserve it, give it an identity. Fire is the phenomena. In every fickle of millisecond (chana), the fire is no longer the same as the previous one, however so appeared the same in our impression. This is the analogy of our impression of there is a "me", "self" independently resided in certain body, which is not. But the Karma (the energy of the fire, all the attributes) will pass on milliseconds after milliseconds, and also interacting with the next conditions to produce new tendency.
It's not easy to describe this concept, and as a student my ability to explain/ to understand is not perfect.

What is an Asura

An answer to this question is in the Khajjanīya Sutta. The Khajjanīya Sutta explains life is comprised of five aggregates, namely: (i) body; (ii) feelings; (iii) perceptions; (iv) mental formations; & (v) sense consciousness. Mental stories about so-called or imaginary 'past lives' are 'mental formations', similar to dreams the mind constructs or manufactures in sleep.
The Khajjanīya Sutta states 'mental formations' about the past should be interpreted as follows:

Any kind of mental formations whatsoever … whether past, future or present, internal or external, gross or subtle, inferior or superior,
  far or near, all mental formations should be seen as it really is with
  correct wisdom thus: ‘This is not mine, this I am not, this is not my
  self.’

As for 'rebirth', the Paticca-samuppada-vibhanga Sutta explains 'birth' ('jati') is the mental generation of the mental idea, view or 'assumption' of 'beings' ('satta').
SN 5.10 explains that, apart from 'view' or 'conceptual thought' (which are mental formations), there are no 'beings' to be found. SN 5.10 also states the idea of a 'being' (or 'soul') is a view held by Mara (Satan).
It follows, as explained in SN 22.85, each time the mind gives birth to the 'self' idea & believes it is a 'self', that is 'birth' ('jati'). To quote:

There is the case where an uninstructed, run-of-the-mill person — who has no regard for noble ones, is not well-versed or disciplined in
  their Dhamma; who has no regard for men of integrity, is not
  well-versed or disciplined in their Dhamma — assumes the body,
  feeling, perception, mental fabrication &/or consciousness to be a
  'self'. That assumption (of 'self') is a fabrication. Now what is the
  cause, what is the origination, what is the birth (jati), what is the
  coming-into-existence of that fabrication? To an uninstructed,
  run-of-the-mill person, touched by that which is felt born of contact
  with ignorance, craving arises. That fabrication (of 'self') is born
  of that.

If the 'self' fabrication keeps arising in the mind, each new fabrication of the 'self' idea is a new 'becoming', a new birth or 'rebirth'.

Most importantly, regardless of how the words 'birth' ('jati') & the myriad terms translated as 'rebirth' are interpreted, the most salient feature of Buddhist rebirth is it is always connected to the results of kamma (actions), i.e., productive of happiness ('heaven') & unhappiness ('hell'). To quote a stock phrase:

'These beings — who were endowed with bad conduct of body, speech &
  mind, who reviled noble ones, held wrong views and undertook actions
  under the influence of wrong views — with the break-up of the body,
  after death, have re-appeared in the plane of deprivation, the bad
  destination, the lower realms, in hell. But these beings — who were
  endowed with good conduct of body, speech, & mind, who did not revile
  noble ones, who held right views and undertook actions under the
  influence of right views — with the break-up of the body, after death,
  have re-appeared in the good destinations, in the heavenly world.'

Unlike the Hindu reincarnation found in the Bhagavada Gita, which states the soul (atman) will always enter a new physical body at death, the idea of 'rebirth' in Buddhism is always connected to the results of kamma or moral efficiency.
Therefore, in Buddhism, unlike Hinduism & unlike the heretical branches of Judaism, 'rebirth' in Buddhism is not 'meta-physics' but, instead, 'morality' about results of kamma.
In other words, even Buddhists that do not believe in life after death still must believe in 'results of kamma' or 'moral rebirth' in order to have right view.
The language used in the Pali scriptures accommodates both views about 'rebirth' since terms such as 'beings' ('satta'), 'death' ('marana'), 'body' ('kaya'), etc, have dual meanings.
As previously stated & quoted, in the older Pali suttas, the predominant view about 'rebirth' is good kamma leads to 'heaven' & bad kamma leads to 'hell'. It seems only in later teachings did the idea of returning as a human being start.

In general, Buddhism teaches all things whatsoever are 'not-self' or, if using Hindu terminology, 'not-soul' ('anatta'). Therefore, Buddhism is contrary to Hindu & later-day-Jewish ideas about transmigration of souls. The Jewish Encyclopedia states:

'Transmigration' of souls (metempsychosis)...This doctrine was foreign to Judaism until about the eighth century, when, under the
  influence of the Mohammedan mystics,  it was adopted by the Karaites and other Jewish dissenters.

As for the pseudo-science of  Ian Stevenson and Jim Tucker, since their claims arise from the studies of literally few children from billions, their claims can be debunked with explanations such as: (i) the child was conditioned by is parents; (ii) the child has a mental disposition or psychic power that can absorbs external ideas; and (iii) mystics with psychic powers are controlling the mind of the child.
For example, the failure of many so-called reincarnate Tibetan lamas, such as Tenzin Ösel Hita, shows such ideas about the reincarnation of souls are spurious or tenuous. In the case of Ösel Hita, it seemed to be not 'transmigration' but child abuse. To quote Ösel Hita:

"At 14 months I was recognized and taken to India. They dressed me in a yellow hat, they sat me on a throne, people worshipped me ... They
  took me away from my family and put me in a medieval situation in
  which I suffered a lot. It was like living a lie."

If we all were really reincarnated souls then we would all remember our past lives or we would all be born with knowledge & experience from our past lives. But, unfortunately, we are all born ignorant, like a blank slate with some natural instincts, and we all must learn how to live & survive in life, as though we all started out anew & fresh.
Some translators of old Buddhist scriptures use the word "transmigration" but this is just a mistranslation.
Similar to the Jewish dissenters, later-day Buddhists created many ideas about reincarnation & even ideas about how 'consciousness' (which is mere sense cognition) is reborn, which probably explains why Buddhism become extinct in India, since it became the same as Hinduism.
Even in the Pali suttas, there are maybe a dozen suttas from thousands (such as the Chariot Maker sutta) that state the Buddha had a literal past life. These suttas are questionable as to their authenticity given they contradict the Khajjanīya Sutta.

In summary, original Buddhism taught the idea of 'self' is merely a mental formation/fabrication born from ignorance and that, in ultimate reality, there is no 'self' to be found. Therefore, the idea that 'my soul transmigrated' or the idea that "I" had a past life is contrary to original Buddhism.

Bhumishu makes a great analogy to fire leaping from one log to the next.  In my studies and understanding, consciousness is often referred to in this way as the “mindstream” in Buddhism.  The mindstream does not have a beginning nor an end as a either would suggest an independent existence of the consciousness apart from reality which would start to head down the road of the nature of a self/soul, etc., which is self-contradictory and an illusion.
Instead, according to Mahayana and Vajrayana/Tantrayana Buddhism (which I believe is the evolved form of Buddhist thought personally), consciousness as mindstream can be viewed as an ocean and that individual manifestations of it, i.e. you and me, are like waves in the ocean that rise and fall.  We can also see it when we look at the impermanence of our own lives - for example, we are not the same person we were 10 years ago, 20 years ago, or even five minutes ago.  In this sense we are born and die moment to moment, millisecond to millisecond.  Buddhism strongly advocates that the idea of a soul (or atman) is nonsensical and is a grasping for permanence in an impermanent existence.  In this light, no, there is no such thing as rebirth or reincarnation as the "self" one supposes will be "reborn" doesn't exist in the first place – however, the energies that make up an individual’s sense of awareness/consciousness may indeed pass on to another “existence” or “rebirth”.
This type of thinking quickly leads to a discussion of karma.  Karma is not a sense of fate or some mystical magical hippie fairy dust (although I think there may be some mystical aspects to it, but that is purely subjective).  It is simply cause and effect.  The things you do and even think affect you which can affect others and your environment, etc., akin to the Butterfly Effect.  In this way, karma can carry on a person's energies (if you will) to other lives beyond their death.  In concrete terms, how your parents raise you and interact with you throughout your life carries on past their death in your own conventional sense of personality and behavior.
On a more mystical level, karma, in Buddhism, leaves an imprint on the eternal mindstream.  Thus, there are aspects of your life as you know it that will, on a subtle level, make "memories" in the mindstream that can carry over to the next life.  In this sense, yes, Buddhism supports a notion of rebirth.
Further down this discussion is what Buddhism refers to as "appreciation for the preciousness of life" or something along those lines.  In a nutshell, this is a meditation on the appreciation of our current life situation - we are born in a human body that can contemplate life and happiness, etc.  We enjoy the comforts of technology improvements both physically and development of freedom and philosophical/rational/scientific thought.  This is in contrast to being born as an animal or in a situation of intense suffering or intense pleasure (perhaps oppressed by slavery or being born in extreme wealth and power).  All of these things enable us to be grateful that we can study Buddhism and ask these kinds of questions.  When we talk about rebirth in this area, the expectation is that the fragments of our consciousness that "return" (if you will) to the mindstream after death may indeed form as a part of consciousness in a future life.  This is not rebirth of the self but merely part of the energy we all possess in the form of memories, etc., but (in Buddhism) these are likely not to be reborn in this human existence but perhaps as an animal or an alien in another galaxy, who knows (although human rebirth can happen and later Buddhism does believe in reincarnation of enlightened beings - i.e. beings that gain enlightenment to the point that they can "traverse" the mindstream to a future human life after death like the Dali Lama or Lama Yeshe reincarnating as Ösel Hita as mentioned in another comment – although I disagree with the assessment of Ösel Hita in that comment).  All this said, most of us (or at least most of our sense of awareness or consciousness) will not be reborn as a human but will be mixed in with the larger ocean of consciousness and will end up as part of an animal or something else, perhaps even part of humanity's emergent global consciousness or whatnot, but this is purely speculation.
So, long story short, Buddhism believes in rebirth and it doesn’t.  If you argue that Buddhism is strictly the Hinayana/Theravada school of thought (which I don't believe) then, as Dhammadhatu mentioned, rebirth is largely disputed.  If, however, you view Buddhism as merely a label to a particular type of evolving Vedic thought that began as Hinayana (enlightenment only for monks) and evolved along with broader human thought to include enlightenment for everyone and following Buddhist logic rationally to conclusions beyond Hinayana (as I do) then rebirth is definitely a thriving concept in Buddhism.
On a scientific level, one can look at rebirth as the conservation of energy.  Where does our conscious energy go after death?  It is certainly not destroyed but somehow dispersed.  On a Buddhist level, one can also do what the Buddha taught even back in the days of the Theravada school.  That is, go and find out yourself.  Meditate on your memories and walk back through them as far back into your childhood as you can.  Once you get there, sit for a while and absorb the experience.  I think you will start to answer your own questions that way - religious dogma is not necessary to tell you what to do or think or believe; your rational mind can explore for itself if you develop the skills of concentration, patience, and wisdom.  This to me is the true beauty of Buddhism – that is, there are foundational tenants but not really any dogmatic thinking by and large.  It is a process, belief, and philosophy of the discovery of reality in all its forms.
Hope that helps!


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How to survive Buddhism ? Buddha, Dhamma and Sangha
I'm observing around me, family and in society. I want to know while Dr. B.R Ambedkar gave the way to peace to Dalit(Backward people) . I could see still my family into ritual other than Buddhism. And also so many people who are just called Buddhism but still following Hinduism rituals. In society, t.v. channels supporting and their relational perspective. I seen in serials they celebrating festivals but never seen celebrating Vesak Day and they calling themselves secular. When Buddhism is an ancient religion and was speeded all around the world very well. I read many present Hinduism temple and mosque was Viharas. And people also wouldn't change their mind. They following myths. I'm really feel very bad about it and for Buddha, Dhamma and Sangha. When it's sole way to the peace.

Sorry, it's not clear to me what the question is. I think you're saying that Dr. Ambedkar gave Buddhism to Dalit people, but that you see Hindu culture (e.g. festivals); but I don't know what your question is ... according to the title the question is something about "survival", but I don't know what.

Survival is that people who to be called Buddhists themselves but following myth and ritual  of Hinduism. That whyt they should be called Buddhists ? That affecting this peaceful religion. As Buddhism was spread very well and with peaceful way ; Brahmin tried corrupt knowledge and history of Buddhism. Many present Hinduism temples was Vihara in early. That's affected Buddha, Sangha and Dhamma.

I see one aspect of your question is practice of rites and rituals much like other religions. This is also important for Buddhism to be socially and culturally integrated, but this does not give you liberation.
Secular Buddhists strip Buddhism of some of the aspects which cannot be conventionally seen (e,g, other realms, life after death) and perhaps some of the aspects not in line with western culture (e.g. respect to the Triple Gem). Accepting and dismissing things beyond your comprehension is a mistake, so would be accepting things which you cannot empirically verify. Until you know something at an experiential level it is best to set them aside.
There were many Buddhist sites in India which perhaps became sites for other religions.

I'm accepting everything about practicing Buddhism . I mean worry about people neither practicing nor believing in Buddhism while they must do seriously (for their own peaceful life). You can see in other religion, If they are from specific religion they practicing only one that they are. But in here Buddhists are just known literally not practicing sole way. They believing in astrology numerology and so on when Buddha never talk about it. People following myth. I worry about what Buddhism's future just because people like this.

In China, Malaysia, Thailand, Japan people believing rituals. I mean they worship Buddha as god and more beyond god , But here In India people just like listen Dhamma and let it go. They don't believe in rituals and rites about Buddhism but they don't listen Dhamma carefully it's importance. Following astrology, numerology and lots of stuff even Black magic. They distracted from the path. I'm just worried about it.  Thank you so much @-}--

If you have found the true heart of Buddhism, you should practise it for your own liberation from the sufferings of this world.
The Buddha never taught all people would or could follow his teachings.

I surveyed the world with the eye of an Awakened One. As I did so, I saw beings with little dust in their eyes and those with much, those
with keen faculties and those with dull, those with good attributes
and those with bad, those easy to teach and those hard, some of them
seeing disgrace & danger in the other world.
MN 26

When once asked: "Would he lead all people to liberation?", the Buddha remained silent.

Master Gotama, when having directly known it, you teach the Dhamma to your disciples for the purification of beings, for the overcoming of
sorrow & lamentation, for the disappearance of pain & distress, for
the attainment of the right method & for the realization of Nibbana,
will all the world be led [to liberation] or a half of it or a
third?"
When this was said, the Blessed One was silent.
AN 10.95

It is sad to see what has become of Ambedkar Buddhism in contemporary India today. For those who do not know Dr. Babasahab Ambedkar, he is the father of the Indian Constitution – a public figure who is far greater and more famous within India than Mathathma Gandhi.   If one could ever call someone a Bodhisatva, it is Dr. Ambedkar. After his own conversion as a disciple of the Supreme Buddha, Babasaheb converted all the rest of his half a million people, by Trisaran, Panchasila and 22 vows. This was a historical event in more ways than one. Never in history half a million were converted to any religion at one time and never had conversion been effected by a lay Buddhist and never ever the Hindu Gods and goddesses were denounced by 22 vows which became the inseparable part of rite of conversion to Buddhism in India, and never before it was declared that all and every Buddhist lay person was authorised to convert other willing person. There used to be rite of Upasampada for conversion as a Bhikku, but for lay Buddhist there was traditionally no rite. Ambedkar started this, as he believed one of the reasons of disappearance of Buddhism from India was absence of such a rite.
My only criticism of Dr. Ambedkar’s declaration of the famous 22 vows (in 1935 at Yeola in Nashik district in Maharashtra) is the mention of Paramitas. In the number 12 of the 22 vows, he said, “I shall follow the Paramitas prescribed by the Buddha.” The TRUE teachings of the Supreme Buddha do not have any mention of the pāramitās and thus ‘Paramita’ is not Dhamma. The pāramitās are only for the Buddhas. The ‘Buddha Vishaya’ and ‘Loka Vishaya’ is not for the disciples. The entire vast infinite universe is Supreme Buddha's “Vishaya Kshetra”. Our lives are too precious and short to waste time on these unwanted topics. Paramita is one such.
Today India has lost the Order of the Gautama Buddha. Those who call themselves as Buddhists have political/social goals as their central component. Furthermore, they have made the Triple Gem impure by worshiping Hindu “Demigods”, by believing in horoscopes, following auspicious times, and even in having a higher regard to being vegetarians [like Devadattha (Buddha’s cousin) & his teacher, Nighanta-Naatha-Puthra] than the Five Precepts.
Thus for those few remaining disciples of the Supreme Buddha it is very difficult in the present day to meet in person a 'Kalyana-Mitta' / ‘Noble (or good) Friend’ in Dhamma. For them I would recommend the Buddhagyan Ashram, as there you can find the Kalyana-Mitta that you seek.   Many in and around this Ashram in India were able to develop confidence in the Triple Gem because the monks there practice the Dhamma truely. Whenever an Indian friend in Dhamma ask for my advice, always my advice to them is to go to the Buddhagyan Ashram even for a week or two as it would be a life-changing experience for him or her.
It is very sad that Dr. Ambedkar passed away too soon before showing the people of India that the Dhamma-Vinaya is our Teacher. Today to help one in the Dhamma path, the Mahamevnawa Buddhagyan Ashram is there. Address : RATTI BIGHA, BODHGAYA-824231, GAYA, BIHAR, INDIA. Phone: 00919006029637

Thank you so much . I need that one Kalyana-Mitta. Even I've to start practicing. And after I'll be good I'll try to change people as I could do. I'm being so emotional for this. But truth never hide so far they have to come back and finally on the way that is Buddhism. Thank you so much @-}--

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Can we still reach loved ones with guidence after they have passed through the bardo into a rebirth?
The question I pose is the same as the title of this post. Any experience or further reading of how to practice this reaching of a loved one to support and guide them after they have passed through the bardo into rebirth.
Thank you
What I mean by reaching....is, I suppose after reading the post below by bhumishu; to send a blessing. Is this received? Now even another question....I have read that there are 49 days in the bardo and the first day is equal to four days which in total will be 52. All of which are merely symbolic. Can someone or you please expound on this? Also, I do have a copy of The Tibetan Book of the Dead which will need to be opened and read again and refereed to again for retained wisdom. Any and all acceptance that can be given that I was unable to be there to guide my Grandmother within the 49 or 52 day time frame according to the practices given in the teachings. This is why I deeply want to assist or send blessings to her that are received by her in whatever or wherever she may be now. Thank you so much!

Please correct me if I'm wrong, I added the [tag:tibetan-buddhism] tag because I think that "bardo" is specific to that tradition (and so I think that you want answers from within the perspective/tradition of Tibetan Buddhism).

What do you mean by reaching?

I edited my original post to clarify the question you asked. Thank you

"Can we still reach loved ones with guidence after they have passed through the bardo into a rebirth?"
If "guidance" you refer to what the book "Tibetan Book of The Death" instructed, then it would be "no". That person is in a new life form, all the possibilities during the bardo stage is conclusive now. In general saying, the bardo lasts max. 49 days. However, you may send blessings to the loved ones any time.

I edited my original post when you are able to share your experience or insight and am new to the forum, so this is the only way that I have figured out how to communicate with those that have contributed to the discussion. Thank you so much..

That is unless they are trapped as an earthbound spirit or ghost, right?

@Monism Pantheist: I'm new to this forum too. It seemed some of the functions are limited in reply thus I put mine to another "Answer".

@Ahmed: It is a big topic "earthbound spirit or ghost". The sutra (I needed to take the pain to find the text) said max. in 49 days, all deceased will "rebirth" into one of the 6 categories: Celestial, Asura, Man, Animal, Hungry ghost, Hell being. Many of those that claimed to be the deceased through mediums are pretenders. These could be "spirit or ghost" of any one of the beings. Those such as fox, snake, tortoise, or trees, if these beings live for hundreds thousands of years, with the fine energy gathered and doing self-cultivation, they could become spirits, too. All is living...

@Monism Pantheist
I read your above added, 1) 49 days or 52 days? I would rather not to stuck with a concrete answer. But it's important to understand the significance of number. 49=7x7, 7 is an important number, we have 7 days a week, 7 colors in the rainbow... 7 is a number for a cycle. In the TTBoD you will find that every 7 days a more significant change. There is another sutra 《佛說入胎經》 which described how the embryo developed inside the womb, also in a 7 days cycle. And for female body, 7 years is a major cycle too, in general, eg, 7x2=14 a girl reached puberty, 7x7=49 a woman had menopause. And 3 is another number for a cycle. It is not easy to determine when exactly a person has left the body been in the Bardo stage. The doctor said heartbeat ceased means deceased, or breathe stopped, but some culture waited until the body is cold, the TTBoD said when the yellow fluid oozed from the body, etc. Thus 52 maybe is a safer indication since normal people do not have the ability to reach and communicate with the one already deceased to confirm when the cycle of leaving the body complete.
2) To "reach" a departed loved one after the Bardo: In Mahayana practice, many Buddhist Monasteries have a place to lit light (candle) for the departed, with his/her name on it. This could be for 1 day, 3 days, 7 days, or 49 days. The other way is to chant the mantra or sutra, and tranferred the merit to the departed. These are more ritualistic. Or to give away/ donate in the name of the departed, or his/her possessions, will add merit. However, in the buddhist teaching, everything is interconnected a thought with feeling is sort of energy, your thinking (blessing) directed to your grandmother will have effect on her, no matter whatever/ wherever she is.
Because the Buddhist view is that we have many deaths and rebirths in eons of kalpas therefore everyone could once be our father and mother, daughter and son, we should have compassion to all, and let go once a kinship ended. It is respectable you cared much about your grandma, however, after you have done all you know and can, that's the best of all.

Bhumishu, I am deeply thankful for your comprehensive and thoughtful response; especially point 2). It has been and is an interesting journey in this life and I want and need to continue to give and send blessings to those, including pets which have gave meaning to my life when I didn't feel any. Imperfectly, I did what I could when they were living and now they need to continue to know in whatever way possible; the deep truth of this fact. Thank you

Also, the link you provided about the significance of 7; it certainly is something I would like to read, but I do not have a clue as to what is says. Any possibility of posting the best english translation link you may possibly know of on the web? : )

@Monism Pantheist: Apologize the late reply. I searched the web but didn't find any English version. It described in detail how "rebirth" happened, from entering the womb, inside the - literally "womb prison" (胎獄), for it's congested, hot, upset by any external discomfort... parallel except modern med unable to show beyond the observable facts. Huge collections of Chinese Sutras only few translated, many eng. tran. may not necessary accurate... however for the historical background - distortion, Chi Sutra for some maybe like a "Made in China" label... big topic...

Bhumishu, you sound like some one I wish to meet. The comprehensive view/insight you described...if found in english please forward along. This something I want and need. I have been without a skilled teacher for 15 years and am lost. The loss of my Grandmother in February and my own immersion back into addiction has left me with the deep need for something of substance. The only place I have ever had this has been with working with animals domestic and wild. They are closer to the truth than any human I have ever meet. This is a substantiated fact. Metta, Kurt

@user10485 [quote]...They are closer to the truth than any human I have ever meet.[/quote] Agree with you. Hope you will get pass the lost, addiction is not the solution. Neither do I have teacher, though am thankful for one who inspired me to learn the Buddha's teaching. I rely most on reading, luckily the Chinese sources are rich. I read original sutras in Classic, which is better than many of the "teachers". From materials English and Chinese, I see the differences, strength, shortage and misunderstanding, I wish to address this, share and discuss with you.

You can send your blessings
But there are few conditions,
Your loved one must be in a life form which can receive your blessings.
Every person is not going to reborn as a human being . Being a human is very rare .
If your loved one reborn as a human or an animal he/she can not receive your blessings.
They can receive only if they reborn as a lower-level(lower than humans/animals)  being .
In Buddhism if someone died , he will be born right after (maybe temporarily for few days and reborn in another life form) , in a way that a dying candle ignites another candle just after its death. The flame is the one which passes , not the candle , the candle can be different. Here , the candle is the life form (human,animal etc...), the flame is the soul that passes after the death.
Conclusion
You can contact your loved ones after death, but it has a one in a million chance .
But if you developed your mind to a certain point , you will be able to see what's going on after someone dies.
Note
Please don't read much books , because it has been a long time and most books have changed , deliberately or by mistake, it is very rare to find books with real Buddhism.
So if you want to learn more I think it's best to learn from a teacher who has a practical knowledge(who has developed the mind to some level) about the path to nirvana.

lasan, from your experience where do I find a true teacher and true readings that express true Buddhism? I have read D.T. Suzuki, have Diamond Sutra, as well as other books including the english translation of the Tibetan Book of the Dead.  There are numerous sanghas with numerous meditaters. Where to find the true discipline? Thank you...

@MonismPantheist from my experience, there are really good teachers in Sri Lanka , and they are very helpful. If possible you can visit that small island to learn . :) , personally I don't learn Buddhism from books.

@lasan There are few raw mistakes I must address: 1) {In Buddhism if someone died , he will be born right after...} this is incorrect, only those who are 'accepted' in one of the Purelands can be born without the intermediate existence "Bardo" (中陰, 中有). 2) {the flame is the soul that passes after the death... } Buddhism invalidated the concept of soul (the biblical idea). To explain this in rough, the flame is the collection of all the acts and senses that symbolized as a form - flame; not as a 'soul' with a solid/eternal identity. (continued...)

@lasan (... continued) 3) {Your loved one must be in a life form... } You don't understand there is no real 'dead', thus every being is always in certain kind of 'life form', incl. the 'Bardo'. In fact the whole cosmos is alive, a stone is a kind of 'life form' but it doesn't got certain senses and categories as a man, or an animal, or a plant, or a bacteria... etc. 4) last, I don't find any proof of what your saying lower/higher life form that determine reached or not reached. The mind 'wave' (念) can act upon anything incl. water, plant... why can't on a lower or higher 'life form'?

@Bhumishu米殊 It's preferable to supply (or to improve, to expand) your own answer, than to use comments to contradict other answers.

all_licenses: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/3.0/


text:
What is meaning of Buddha and how he called Buddha?
By marathi language "Buddhi" means intellectual so what is meaning of "Buddha" or is same as Buddhi? Does people started call him Buddha ?

Does people started call him Buddha ?
It's according to the suttas that he told people to remember him as "Buddha". For example, at the end of the Dona Sutta (AN 4.36):

Remember me, brahman, as 'awakened.'
... and so, brahman,
I'm awake.

Alternatively the Dharmafarer translation of this sutta:

Therefore, brahmin, remember me as the Buddha.”
... therefore, brahmin, am I buddha.

The Pali for that last line:

tasmā buddho’smi brāhmaṇâ ti

"Buddha" isn't the only word used; for example there's also tathagata.

Definition of Buddha based on Pali Dictionary is here:

Buddha Skt., Pali, lit., “awakened one.”

The Wikipedia entry is here:

The word Buddha means "awakened one" or "the enlightened one".
Hypothetical root budh "perceive" 1. Pali buddha – "understood, enlightened", masculine "the Buddha"; Aśokan (the language of the Inscriptions of Aśoka) Budhe nominative singular; Prakrit buddha – ‘ known, awakened ’; Waigalī būdāī, "truth"; Bashkarīk budh "he heard"; Tōrwālī būdo preterite of bū, "to see, know" from bṓdhati; Phalūṛa búddo preterite of buǰǰ , "to understand" from búdhyatē; Shina Gilgitī dialect budo, "awake"; Gurēsī dialect budyōnṷ intransitive "to wake"; Kashmiri bọ̆du, "quick of understanding (especially of a child)"; Sindhī ḇudho, past participle (passive) of ḇujhaṇu, "to understand" from búdhyatē, West Pahāṛī buddhā, preterite of bujṇā, "to know"; Sinhalese buj (j written for d), budu, bud, but, "the Buddha".

Buddha means one who understood or awakened. This understanding / awakening is based on intelligence gained.


text:
What is the difference between a nature and a behaviour?
I believe that every person comes with a nature in-built into self and creates/maintains his/her own behaviour into self.
So, may I call it fate? Or, is there more I have to learn about? How does buddhism take it? I wish to get personal views, only.

Actually, in fact I am in need to unleash the difference.

I welcome such a discussion and find this question enjoyable, especially because it merits personal views and not just carved-in-stone texts.
Even from a scientific point of view, defining "what is nature (natural)?" has been a difficult task that has been evolved in different fields such as meta-physics, astronomy, mathematics and religious studies, etc for many many years.
A simple question as follows could solicit long discussion, which could bring up hundreds of other questions that would eventually become a "chicken or egg?" problem:
Is acid rain natural?
If one thinks in her own logical way that has been taught in school, the answer is Yes and No.
Some say it is natural in a sense that it is "cause and effect".
While some say it is not, because it shouldn't exist.
Putting science aside and leaning back on my own personal view of what I have read/learnt in Buddhist books and articles over the years:
One thing we could be sure of:
We are all born with a good heart and will. Having a good heart and will not in a sense that we start making donations to charities, look for someone to save, or counter others whose deeds we deem "bad".
Rather, we were all born a "Buddha". But we are not (yet), due to "senses (feelings)" that we so quickly acquire the second after birth.
Examples:
It tastes good.

He is handsome.

She looks beautiful.

I must do it against all odds to uphold and thus protect this, because of my tradition. (clinging)

I hate ....

It is so funny (laughters).

From my own thinking based on books that I have read, people and nature that I have met and observed (including observing my own self, too), to be "natural" (nature) is to lose those layers of "cocoons" that bar us from being a Buddha since birth.
Those layers being - senses and feeling - hence thoughts (judgements, logic, biases, preferences, liking, disliking, stubbornness, heroism, etc etc).
Other words, following the buddhist path is to become one with everything and all (even an ant is of greatest "importance" in its own existence in this space).
The preceding on "Nature" is only my personal view based on my own experience and thinking.
The following brings us to "Behavior":
Behavior, in my opinion, is what has been mentioned above - senses and feelings - all these surmises to thoughts.
Thoughts bind you to do or not do something regardless whether or not it is "right" or "wrong" or "good" or "bad".
It becomes a fuel that "supports" your actions based on senses and feelings.
Other words, behaviors are learnt since brith though sense, feeling - thus thoughts.
Examples:
"My mother told me...."

"I was trying to be nice to her, but she, nonetheless, refuses to go out with me. I guess all girl with short hair are mean."

"It feels so good, even feels better in the winter....." (senses)

"I loved him so much, although I knew he has wronged me. But I just couldn't help it, I hope he will love me one day and sees finally what I have been doing to myself out of love of him.."

All of the above behaviors could be unlearnt and thus undone, usually though:
"My mother was wrong; now I know because ..."

"No, not all girls with short hair are mean; my neighbor has short hair and she is very friendly"

"You know what, I have read that even it feels good, one shouldn't do it because ......"

"I guess I was naïve; he was not for me, now I met the greatest man of my life, who cares for me......"

The above are examples of "counter-behaviors".
In buddhist sense, the above is not the way we should lead ourselves to.
We shouldn't need to find a counter-behavior to eliminate a behavior.
Other words, we should not pick up the behavior from the beginning.
Example:
One does action (behavior) A.
Years later, one finds that action (behavior) A is bad, then she finds (learns) action B to counter action A.
1 + (-1) = 0

It would stay so, as long as action B "prevails"; if one day, through time and experiences, you find action B unpleasant or you simply lose your will to hold on to it, you revert back to carrying out action A.
In short, Buddhism teaches us to not pick up "action A" or behaviors through senses and feelings in the first place, thus eliminating the "need" to find a counter-action such as action B, because the process is clinging and un-clinging, which disturbs our peace of mind and our "Nature" to become one with everything.

Thanks. thats what i can sense, feel and learn. if you have any online book or article describing 'why here are different-2 behaviour' kind of thing, then please paste the links in comment. Regards

Inbuilt is nature and Reaction of mind toward other is behavior

from what i know, I would call it
Avijja or ignorance.

nature in-built into self and creates/maintains his/her own behavior into self

we are born without the knowledge of how to get out of sufferings the right way (not knowing four noble truths is ignorance)

Inbuilt is also a quality/quantity someone had being practicing all over the past lives of oneself. Due to practicing the recurring actions, learnt and acquired knowledge and attitudes during past lives, you are who you are now and you have chemistry now that makes you and your own nature.
Behavior is present actions. Current knowledge and attitudes have major influence upon it but it is also based on personal nature (the collected effects of past actions). That is why you can use the word fate because nature and behavior can make your life predictable unless you make turning point and changing direction.
Buddhist teachings can help you to learn more about you and determine yourself whether you are going more sufferings direction or going to Nirvana. There are information and instructions in Dhamma for you getting the right direction to live with less sufferings and finally end of all sufferings. So in terms of personal practice, personal nature (past experiences collected) is not anymore major factor of your future if you can adapt/adopt Buddhism behavioral practices. You can maneuver yourself on right path and get the goal.


text:
What is it like to perceive without 5 Skandas?
My understanding of Nibbana is a person who has overcome 5 skandas.
I could not perceive the state as we are constantly bombarded with internal and external stimulations which makes me assume that this state can never be achieved and only an incremental change towards nibbana can happen. This leads to another interesting observation, if 5 skandas are overcome, does one really need a body? If body is not needed, then is Nibbana attained only at death?
What is it like to be without skandas?

BTW are you the same as: http://buddhism.stackexchange.com/users/5016/8ck8 in which case it is best to merge a/c and use one account.

yes i couldn't login to old user account

Maybe you can ask SE to sort it and you can also more to a registered A/C

Nibbana is the 5 skandas have overcome the idea of a "person" & "who".
The Pali scriptures define Nibbana as the end of greed, hatred & delusion and occurring to a living conscious mind. The following is merely one teaching from many:

Here a bhikkhu is an arahant, one whose taints are destroyed, the holy life fulfilled, who has done what had to be done, laid down the
  burden, attained the goal, destroyed the fetters of being, completely
  released through final knowledge. However, his five sense faculties
  remain unimpaired, by which he still experiences what is agreeable and
  disagreeable and feels pleasure and pain. It is the extinction of
  attachment, hate and delusion in him that is called the
  Nibbana-element...
Iti 44

Can you please expand on "the idea of a person & who"?

A "person" or a "who" is a idea, view or thought  created by the sankhara khandha. Therefore, in enlightenment, the idea of a "person" disappears, which is Nibbana. In other words, a "person" does not attain Nibbana. What attains Nibbana is the personless aggregates. You can read these links about the "who" and a "self": http://www.accesstoinsight.org/tipitaka/sn/sn12/sn12.012.nypo.html & http://www.accesstoinsight.org/tipitaka/sn/sn22/sn22.081.than.html & http://www.accesstoinsight.org/tipitaka/sn/sn05/sn05.010.bodh.html

If body is not needed, then is Nibbana attained only at death?

According to the Pali text references are made to Nibbana as sopadisesa and anupadisesa. These, in fact, are not two kinds of Nibbana, but the one single Nibbana, receiving its name according to the way it is experienced before and after death. - Buddhism in a Nutshell - Nibbana

What is it like to be without skandas?

You cannot exist without skandas. Nibana is like the flame blowout.

I could not perceive the state as we are constantly bombarded with internal and external stimulations which makes me assume that this state can never be achieved and only an incremental change towards nibbana can happen.

Yes. It is a gradual process where you pass multiple stages before the glimpse of Nirvana and also after until final Arahatship.

"What's it like to be without the five skandhas?"
If you read the Heart Sutra, "Avalokiteshvara saw the five skandhas to be empty [of essence, empty of having a self, selfless, empty of an 'independent individual'].
This means that it is not the five skandhas that we are trying to abandon, we are simply trying to see them clearly and without beliefs.
The Five Aggregates or Heaps or you might even say Piles or Sediment  are:

Form (or we can say "matter")
Feeling (physical awareness)
Perceptions (sounds, smells, tastes, touches, identified and pre-identified [or without labeling])
Formations (such as birth, death, figments of continuity over moments)
Consciousness

With enough relaxed meditation, relaxing the speech and the thinky/discursive mind, one can collect and attune their pervasive-attentiveness to an investigation of self and if all the aggregates are truly selfless, as is taught.
Metta and joy.  Just offering some notes to aide, perhaps they will be helpful.

What is it like without the 5 Skandas?

Speaking from personal experience, I would say it probably a place of healing. It's not a "black and white" state (it doesn't have a clear demarkation). When a meditator focuses on the present moment, they lose all sense of self and the five aggregates that you mention. They don't feel anything when they are in that state, but only when they "return" do they feel the benefits of escaping. The first thing they notice upon returning is the effects of the absence of the constant chatter of the mind. It's like there was a jackhammer constantly running in the background and for the duration of the session it had stopped. It's almost like being asleep, but its different. Letting go is difficult though.

if 5 skandas are overcome, does one really need a body? If body is not needed, then is Nibbana attained only at death?

I'm not sure about this one. The Buddha encourage one to stay away from metaphysics.

Purification..., Liberation..., Nibbana...
The Buddha Himself in the Nibbana Sutta, Udana 8.1:

"Nibbana... that dimension where there is neither earth, nor water,
  nor fire, nor wind; neither dimension of the infinitude of space, nor
  dimension of the infinitude of consciousness, nor dimension of
  nothingness, nor dimension of neither perception nor non-perception;
  neither this world, nor the next world, nor sun, nor moon. And there,
  I say, there is neither coming, nor going, nor stasis , neither
  passing away nor arising: without stance, without foundation, without
  support.  This, just this, is the end of dukkha."


text:
Getting Started
How do I get started on my journey to become Buddhist? I'm familiar with the basics and really connect with the teachings I know of so far on a personal level. I need some guidance as to what I should do now...

You approach should be pariyatti (learn), patipatti (practice) and pativedha (experience / validate)
To learn you can read. Perhaps a good starting point will be:

In the Buddha's Words: An Anthology of Discourses from the Pali Canon (The Teachings of the Buddha) by Bhikkhu Bodhi
Sutta translations by Piya Tan.

Also you can find a course or teacher:

Vipassana (as taught by S.N. Goenka)
World Buddhist Directory

Start with a Vipassana retreat. Buddha sates clearly that the goal is the attainment of Nibbana by the practice of Vipassana.
I am fan of Thai-style (Ajahn Tong) Mahasi tradition (don't worry if this means nothing to you), they do a 3-week "basic course" which is suitable even for people who never meditated before. Something like that will give you a good taste how meditation makes you a better person and will build up your confidence (in the practice and in your ability to meditate), something books will never give you.
Good luck!

Let's deconstruct what you are saying.  You find the teachings resonating with you.  You feel you've got a handle on the basics.  It would seem like you've got some faith in the Buddha and you are beginning to feel the pull of the dharma.  Well, what's missing?  The next step for you is to find a sangha!
I cannot overstate the importance of a community when it comes to your practice. It really keeps you honest about your progress.  There is a major tendency for people to live their Buddhism in their heads.  While sutra study and meditation are both extremely important, neither is worth a damn unless you can integrate those practices with those around you.  Enlightenment doesn't happen in a vacuum located somewhere between your right and left ear.  It happens in the world and in your relationships with others.  The sooner you can begin that integration, the better off you'll be.
In our digital age, we are pathologically cut off from others.  This is the exact opposite of what the Buddha taught.  Compassion, loving-kindness, and wisdom are hardest yet find their fullest expression face to face.  And as an aside, remember that the sangha isn't some thing out there that will always be waiting for you to join somewhere down the road.  YOU are the sangha.  Unless you participate in it, it doesn't exist.

I would suggest you to take one or two sutras to read yourself first. The Buddhas said his life merges into the sutras. It's the purest way to get your first hand understanding, before joining or listening to any school anyone. Since opinions and viewpoints are flooding thanks for the advance of medias, the purity of the Dharma and a good teacher is not easy to find. To begin with, Heart Sutra, Jakata although some said it's stories (made up by others). Personally I like to read Lotus Sutra, Surangama Sutra, Diamond Sutra (very difficult to understand), Vimalakirti Sutra, Sutra of Perfect Enlightenment, Lankavatara Sutra, I may begin Dhamapada which I read few lines, seemed like a very easy beginner text but dived into the meanings underneath the words one will get the nectar. I found that reading the original text is far easier since the great men's minds had infused into their words. Translations, explanations, elaborations etc. don't always make them simpler, unless necessary. Here "original text" I mean Classical Chinese, unfortunately I haven't learnt Sanskrit yet.

Start with the Digha Nikaya, I would say. It is the Pali Canon's 'introduction' to the Dhamma. There are two really good websites for this:
https://suttacentral.net/dn
http://www.accesstoinsight.org/tipitaka/dn/index.html
If you like to get a hard copy, then you can't beat Bhikkhu Bodhi's (Maurice Walsh's) translation!
https://www.amazon.co.uk/Long-Discourses-Buddha-Translation-Digha-Nikaya/dp/0861711033/ref=sr_1_1?ie=UTF8&qid=1478265250&sr=8-1&keywords=digha+nikaya
If you are a heavy rationalist then also read Nagarjuna's 'Fundamental Wisdom of the Middle Way', preferably the Garfield edition, as it gets misinterpreted quite a lot and he gets it right!
https://www.amazon.co.uk/Fundamental-Wisdom-Middle-Way-Mulamadhyamakakarika/dp/0195093364
(I am such a rationalist, and for the first year of getting through the Digha Nikaya, with the cosmology and gods found in some Suttas, made me read too much into the similarities between 'original Buddhism' and other faiths.. after reading Nagarjuna that wasn't as much of a worry!)
I would say don't explore Mahayana scriptures too much (beyond Nagarjuna), until you have gotten through some of the Pali Canon. It is the oldest of the old, likely very very close to what the Buddha spoke and there is little in it which confuses.
If you want a lighter load then the above, get the Dhammapada and the Sutta Nipata. The latter is considered one of the oldest parts of the Pali Canon, and is at the very least very similar to the Buddha's Dhamma.
https://www.amazon.co.uk/dp/1586380206/ref=pd_lpo_sbs_dp_ss_2?pf_rd_p=569136327&pf_rd_s=lpo-top-stripe&pf_rd_t=201&pf_rd_i=1590303806&pf_rd_m=A3P5ROKL5A1OLE&pf_rd_r=Q8V4YF3PA0DHYFPS170Z
https://www.amazon.co.uk/Sutta-Nipata-Group-Discourses-H-Saddhatissa/dp/0700701818/ref=sr_1_2?s=books&ie=UTF8&qid=1478266004&sr=1-2&keywords=sutta+nipata
Most importantly, meditate! Digha Nikaya 22 gives a long and detailed analysis of how to meditate https://suttacentral.net/en/dn22 .. I find the commute to be a good time to meditate (some earphones can kill the noise, and overall those journeys are very impersonal - a strangely 'secluded' space imo!)

According to the instructions of the Buddha Himself in the Anapanasati Sutta (MN 118):
Sit down comfortably and breath...

... "Breathing in long, he discerns, 'I am breathing in long'; or
  breathing out long, he discerns, 'I am breathing out long.' Or
  breathing in short, he discerns, 'I am breathing in short'; or
  breathing out short, he discerns, 'I am breathing out short.'He
  trains himself, 'I will breathe in sensitive to the entire body.'
  He trains himself, 'I will breathe out sensitive to the entire body.'
  He trains himself, 'I will breathe in calming bodily
  fabrication.'He trains himself, 'I will breathe out calming bodily
  fabrication.'
"He trains himself, 'I will breathe in sensitive to rapture.' He
  trains himself, 'I will breathe out sensitive to rapture.' He
  trains himself, 'I will breathe in sensitive to pleasure.' He trains
  himself, 'I will breathe out sensitive to pleasure.'He trains
  himself, 'I will breathe in sensitive to mental fabrication.'He
  trains himself, 'I will breathe out sensitive to mental fabrication.'
  He trains himself, 'I will breathe in calming mental fabrication.'
  He trains himself, 'I will breathe out calming mental fabrication.'
"He trains himself, 'I will breathe in sensitive to the mind.' He
  trains himself, 'I will breathe out sensitive to the mind.'He
  trains himself, 'I will breathe in satisfying the mind.' He trains
  himself, 'I will breathe out satisfying the mind.' He trains
  himself, 'I will breathe in steadying the mind.' He trains himself, 'I
  will breathe out steadying the mind.' He trains himself, 'I will
  breathe in releasing the mind.' He trains himself, 'I will breathe out
  releasing the mind.'
"He trains himself, 'I will breathe in focusing on inconstancy.'
  He trains himself, 'I will breathe out focusing on inconstancy.'
  He trains himself, 'I will breathe in focusing on dispassion
  [literally, fading].' He trains himself, 'I will breathe out focusing
  on dispassion.' He trains himself, 'I will breathe in focusing on
  cessation.' He trains himself, 'I will breathe out focusing on
  cessation.' He trains himself, 'I will breathe in focusing on
  relinquishment.' He trains himself, 'I will breathe out focusing on
  relinquishment"


text:
sutta reference: forbidding to call the Buddha by name
I've heard that there are suttas where the Buddha forbade people to call him by his given name. Which suttas are these?

This first occurred when he met the five ascetics after the enlightenment when they started calling him by his name Gotama before teaching his earliest discourse, Dhammacakkapavattana sutta.

Bhikkus, do not address me by the name Gotama nor as a friend. I have
  become a Perfect One, worthy of the great reverence.

Source: http://www.buddhanet.net/pdf_file/damachak.pdf page 56

This is found in the Ariyapariyesana Sutta, the Bodhikumāra Sutta and any other suttas that describe the Buddha's search for awakening.

Then, wandering by stages, I arrived at Varanasi, at the Deer Park in Isipatana, to where the group of five monks were staying. From afar
  they saw me coming and, on seeing me, made a pact with one another,
  (saying,) 'Friends, here comes Gotama the contemplative: living
  luxuriously, straying from his exertion, backsliding into abundance.
  He doesn't deserve to be bowed down to, to be greeted by standing up,
  or to have his robe & bowl received. Still, a seat should be set out;
  if he wants to, he can sit down.' But as I approached, they were
  unable to keep to their pact. One, standing up to greet me, received
  my robe & bowl. Another spread out a seat. Another set out water for
  washing my feet. However, they addressed me by name and as 'friend.'
So I said to them, 'Don't address the Tathagata  by name and as "friend."


text:
What is passed from life to life in the process of rebirth?
As a practising Buddhist, I am often asked this question: what is passed from life to life in the process of rebirth?
I have several answers to this depending on my audience - e.g. lessons to be learned, experiences to be resolved or, simply, one's own personal cockpit-style 'black box' of all that has been seen, heard, experienced etc in previous lives.
To what extent do colleagues believe that 'personality' or 'behavioural tendencies' should also be included?
I welcome your views. My question is directed at any practitioner of Buddhism, Theravadan or otherwise.

In the Pali suttas, I have not read anything about a "life to life" process of rebirth. In the Pali language, the word for "life" is "jiva". Where as the words often erroneously translated as "past lives" are "pubbe nivāsa", which literally mean "previous homes" & is often more accurately translated as "past abodes", as follows:

Ye hi keci, bhikkhave, samaṇā vā brāhmaṇā vā anekavihitaṃ pubbenivāsaṃ anussaramānā anussaranti sabbete
  pañcupādānakkhandhe anussaranti etesaṃ vā aññataraṃ
Bhikkhus, those ascetics and brahmins who recollect their manifold past abodes all recollect the five aggregates subject to clinging
  or a certain one among them.
Any kind of aggregate, whether past, future or present, internal or external, gross or subtle, inferior or superior, far or near, all
  should be seen as it really is with correct wisdom thus: ‘This is not
  mine, this I am not, this is not my self.’
SN 22.79 translation Bhikkhu Bodhi

Therefore, the many suttas that mention the Buddha recollecting his "past lives" are actually about the Buddha recollecting his "past homes/abodes", which, in respect to suttas such as the   Hāliddikāni Sutta & SN 22.79, may have an entirely different meaning to "past life times".
The above said, the general principles in the Pali suttas refer to the "death" ("marana") of one "body" ("kaya") and, if enlightenment does not occur, the "taking up" of (attaching/clinging to) another "body" ("kaya").
The words "marana" & "kaya" do not necessarily mean "physical death" & the "physical body". "Kaya", which also means "collection" or "group", can refer to a certain set of five aggregates (e.g. five aggregates affected by alcohol, which manifest as a happy person or happy being/satta). When those five aggregates or that state of 'being' ('satta'; refer to SN 23.2) ceases, one "kaya" & "satta" dies ("marana) & a new "kaya" & "satta" arises (e.g. a new collection of five aggregates & a new state of being that have a headache & sickness or addiction due to drinking too much alcohol).
In conclusion, in the same way an addiction to alcohol is developed, what passes from one "body" ("kaya"; "collection") to another "body" ("kaya"; "collection") is craving & its associated underlying tendencies/habits ("anusaya") & effects ("vipaka"). The short answer to the question is: "craving".
Thus the Pali suttas state:

Vaccha, when a being sets this body aside and is not yet reborn in another body, I designate it as craving-sustained, for craving is its
  sustenance at that time.
Kutuhalasala Sutta

What is passed from life to life in the process of rebirth? Kamma. As taught in AN 5.57:

A disciple of the noble ones considers this: 'I am not the only one who is owner of my actions[Kamma], heir to my actions, born of my actions, related through my actions, and have my actions as my arbitrator; who — whatever I do, for good or for evil, to that will I fall heir. To the extent that there are beings — past and future, passing away and re-arising — all beings are the owner of their actions, heir to their actions, born of their actions, related through their actions, and have their actions as their arbitrator. Whatever they do, for good or for evil, to that will they fall heir."

Ven. Nyanatiloka further explained in his "Kamma & Rebirth":

According to Buddhism, there are three factors necessary for the rebirth of a human being, that is, for the formation of the embryo in the mother's womb. They are: the female ovum, the male sperm, and the karma-energy (kamma-vega), which in the Suttas is metaphorically called "gandhabba," i.e. "ghost," or "soul." This kamma-energy is sent forth by a dying individual at the moment of his death. The father and mother only provide the necessary physical material for the formation of the embryonic body. With regard to the characteristic features, the tendencies and faculties lying latent in the embryo, the Buddha's teaching may be explained in the following way: The dying individual, with his whole being convulsively clinging to life, at the very moment of his death sends forth kammic energies which, like a flash of lightning, hit at a new mother's womb ready for conception. Thus, through the impinging of the kamma-energies on ovum and sperm, there appears just as a precipitate the so-called primary cell."

your comment includes a reference to the existence of a "soul". Isn't anatta, no-self, no-soul central to buddhism?

That's why Ven. Nyanatioka put them in quotes to signal the colloquial and inaccurate use of the term. He did use the more accurate and appropriate term that is in accordance with Buddhism, which is kamma-energy (kammaVega). And that's also why I put Kamma as the answer.

It seems to me that you are describing that which passes as a sort of possession. "I" have it now, and when I pass away, it will be received by some other living being. we can imagine other things that are transferred in a similar way. wealth, a house, any kind of property really, the atoms and minerals of which my body consists. when I pass away, someone else may inherit them. but if that is so then in what motivates the talk about reincarnation? We don't talk about a series of heirs to some material fortune as reincarnations of one another. why justifies such talk when it comes to "energy"?

The new "you" in this life is not completely the same as the one in previous life NOR completely different from him/her. Whether you like the idea or not, you, me, and everyone else were born with a kammic "inheritance" from the dude or the girl before us. The Buddha made it abundantly clear in MN 135 (https://suttacentral.net/en/mn135). So, instead of question about "justice", or "fairness", or whatnot, the fact is that it is here with you now regardless of what you want to think. So what youre gonna do about it? It's up to you to conduct yourself in ways in accordance with the Dhamma or not.

what is passed from life to life in the process of rebirth?
Information.

why bother then about liberation in a future life? whose life is it?

whose life is it now?

Nominally mine.

lol - so, should it not surprise you, that if you think so now, then in the next life it will also be "yours"

In what way would that next life be "mine" anymore than the life of anyone else who might live in the future would be "mine"?

@nir you're doing things today to ease the suffering you will experience tomorrow. This life isn't "you" now and it isn't "you" tomorrow but you're still concerned about tomorrow. In the same way you should be concerned about a future life.

@nir why is the current life nominally yours any more than it is nominally the life of people living in the present? I think you might be confusing not-self with non-existence.

@Huge, my life today AND tomorrow are both nominally mine. I am told that I should be concerned about a future life and I am asking in what way would a next life be mine, and if that question is difficult to make sense of intuitively, then I ask In what way would that next life be "mine" anymore than the life of anyone else who might live in the future would be "mine"? If you insist that there is a transcendent sense of identity which continues through reincarnations, then how does this belief conform with the concept of no-soul or anatta?

Lol. Nir, the lives do not belong to anyone, it is by mistaken identification that a life becomes mine. But when that does happen, the experience is pretty consuming and engrossing, the pain is pretty real. So just like "you" care about this life of "yours" you should care about a future life of "yours" , and about all other lives.

Rebirth is happens mometerity through the process of Momentary Dependent Origination (ekaccittakkhanika-paticca-samuppada). So you die and reborn multiple times in a split second. At physical death also something similar happens. The aggregates passes away and arise but in this case aggregates pass away in one body and arise in another.
For a more details explanation with additional references please see this answer

Supreme Buddha is the best example of that of a person developing a knowledge which enabled Him to read past and future lives. For skeptics, and for those of other faiths of course, one may have to give examples of what modern psychics have given, or recorded evidence of ghostly phenomena, or of spirit communications that one get to hear or experience, to explain rebirth.
This is never a question for ones who have gone far in this road less traveled, and the very reason that they went the distance is that they accepted rebirth as an evidentially verifiable fact, never for one moment questioned it. One sure thing is no one will ever come forward to prove to the worldlings – those who are absorbed by worldly pursuits and pleasures – and the skeptics, that this doctrine of rebirth can be proved experimentally.It is never going to happen.
These individuals that I mentioned above are the “Arahant disciples” of the Supreme Buddha – the ones who have found out experientially that they will have no rebirth again. It is because these Noble Ones have overcome the cause for rebirth, and the Patticca Samuppada (Law of Cause and Effect) has been defeated.  They have had first-hand knowledge that there is no birth due to Bhava, as there is no formation of Karma to result in a birth (“Bhava paccaya jāti” as noted in Patichcha Samuppada) for Arahants. This is why Arahants are completely free from being born again, are the only ones to know of this truth.
As per the scriptures, it is the flux-of-consciousness, from a past life (Viññaña) that goes onto start of another life. Viññaña never exist independently – in and of itself – but always with Nama-Rupa:

'Were consciousness, Ananda, not to fall into the mother's womb, would mind-and-body (nama-rupa) be constituted there?' 'It would not, Lord'. 'Were consciousness, having fallen into the mother's womb, to turn aside from it, would mind-and-body come to birth in this present state?'. 'It would not, Lord.' (D. II. 62-3)

It is erroneous to say that consciousness (Viññaña a) is able to 'break free' from  ‘nama-rupa’. (Here nama is used to refer to all aspects of mind except consciousness itself.) Therefore simultaneous with the arising of rebirth-consciousness there come into being mind and body (Nama-rupa). The six senses (Salayatana) are the inevitable consequences of mind and body. Because of the six senses contact (Phassa) sets in. Contact leads to feeling (Vedana). Dependent on feeling arises craving (Tanha). Craving results in grasping (Upadana). Grasping is the cause of Kamma (Bhava) which in its turn, conditions future birth (Jati). Re-Birth is the inevitable cause of old age and death (Jara-marana).

The only "things" that persist from rebirth to rebirth IMHO are the potential effects of unfruited karmas, which together constitute the continuity of the mind stream. These are non-manifest potentials, not "things" (hence the quotation marks). Thus, there is no "thing," no atta that continues from rebirth to rebirth. Since there is no effect without a cause, and no cause without an effect, every intentional thought, word, and deed that has not yet resulted in an effect at death results in rebirth and consequent experience. This continues until (a) non-intention results in the cessation of new karmas, and (b) all prior karmas have been exhausted, either by fruition or extermination through meditation.

My understanding of the Theravada perspective:

what is passed from life to life in the process of rebirth?

Depending on what one means by "passed", the stock answer is there is nothing passed from one life to another.
If something passes from one life to another (be it memories, consciousness, karma, etc), than that something should be regarded as one's Self. However, the Buddha's admonished (sometimes, strongly, see MN 38) when someone say his teachings promulgate that some substance can be observed to go through rebirths.
However, the Buddha also said we are heirs of our karma:

“ Bhikkhus, beings are the owners of their kamma, the heirs of their kamma; they have kamma as their origin, kamma as their relative, kamma as their resort; whatever kamma they do, good or bad, they are its heirs.
-- AN 10.216

The difficulty with grasping this subject intellectually is the doctrine of anatta/no-self and buddhist doctrine of karma. Thus, the puzzle:

if there's no substance that persists, how could we say that something passes from life to life?
But, if there's no such substance, why the Buddha rejected the idea that physical death is simply the end and talked about "beings appearing at X after death"? And what does it mean to "inherit" karma?

Generally speaking, if we say that karma is what is passed from life to life, then we are turning karma into a substance that persists: saying this is roughly the same as making karma the Self, the Soul. Thus, many avoid saying something of the sorts.
Consider Bhikkhu Bodhi's words about the word "rebirth":

The Buddhist term for rebirth in Pali is "punabbhava" which means "again existence". Buddhism sees rebirth not as the transmigration of a conscious entity but as the repeated occurrence of the process of existence. There is a continuity, a transmission of influence, a causal connection between one life and another. But there is no soul, no permanent entity which transmigrates from one life to another.

So, an answer here is that there's no substance that is passed from life to life, instead there is a causal connection, a process of influence. If the fetters have not being put to an end, after death there's continuity of experiencing dukkha, continuity of experiencing samsara.