The simplest form of rebirth is a usually unending cycling between this world and another world. Richard Gombrich (who has collaborated with Obeyesekere in the past) has highlighted the work of Polish Sanskritist Joanna Jurewicz which shows that contrary to prevailing views there is evidence of just such a belief system in the Ṛgveda: the brahmin goes to the world of the fathers for a period after death and then returns to this world. Jurewicz identifies a single verse in a late hymn which appears to confirm a belief in this kind of rebirth. The late timing suggests that the idea comes not from the group who wrote the Ṛgveda, but rather than the they picked it up after they had been in India for some centuries. 
The simplest form of rebirth eschatology is not moral, rebirth is not dependent on behaviour and so the other world is not differentiated, and this kind of rebirth is the commonest around the world. As soon as morality is introduced into the picture the other world bifurcates into a place of reward, and a place of punishment. In this model good deeds cause one to be reborn in heaven for a period until the merit of the previous life is exhausted, when one returns to this world. This morality need not be ethical. For instance in the morality of brahmins one's destination after death was dependent on proper ritual behaviour, not on ethical behaviour. Just as for centuries Hindu morality focussed on doing one's duty, rather than on one's behaviour more generally (a central theme in the Bhagavadgīta).
A further development occurs when the rebirth destination in this world (as opposed to the other world) is determined by morality in the previous life. This is roughly the situation of the rebirth theories in the early Upaniṣads: Bṛhadāranyka (BU), Chāndogya (CU), and the Kausitaki (KauU).  The 'doctrine of the fires' maps out a relatively complex set of possibilities. On death the one who has understood the identity of ātman and brahman goes to the gods and then onto brahman and does not return . The one who has carried out the sacrifices (i.e. a brahmin who follows the pre-Upaniṣadic religion) goes to the world of the fathers and is eventually reborn as a human (which is the old simple cycle). The third possibility is for everyone else and they are reborn as a śudra or an insect - they don't have an account for the other classes, or any women.
The ethicization of rebirth changes the model substantially into what Obeyesekere calls a karma eschatology - something which appears to be unique to India. This is where one's ethical actions (karma) determine one's next rebirth (though confusingly karma meant ritual action to the brahmins). Although there are hints at an ethical rebirth in BU, the idea is first found fully articulated amongst the śramaṇa groups. Some scholars have taken this to mean that the idea originated amongst śramaṇas and was only later adopted by brahmins, and argue that BU especially shows this absorption in process of happening since it presents different patterns of rebirth. The fact that the ideas about rebirth are presented by kṣatriyas in BU and CU helps to reinforce this interpretation.
In earlier models rebirth was an endless cycle, which came to be called saṃsāra - meaning 'continues to go on'. This idea must have persisted into the Buddhists period even though middle Vedic period texts like the Śatapatha Brāhmaṇa (ca 8th-6th century BCE) mention the possibility of escape from the cycle of 'redeath' as it is called there. We know this because many of the Buddha's teachings are given in terms of an escape from saṃsāra, where saṃsāra is precisely this beginningless, endless cycle of birth and death. Buddhists were not the only group teaching an escape from saṃsāra, and this seems to have been one of the most important religious paradigms both at the time, and subsequently. In the early Upaniṣads, as I have mentioned, escape from the cycle was conceived of in terms of 'going to brahman', or 'union with brahman': brahmasahavyata. I have discussed one of the Buddhist responses to this belief in the Kevaddha Sutta in an earlier post. Here we find the Buddha claiming:
I know Brahmā, and Brahmā's domain, and the way leading to Brahmā's domain.The result was not to deny the escape from saṃsāra in terms of the path to brahman, but to adopt and adapt it. At present I do not think the very distinctive nature of the brahmavihāra meditations with respect to other styles of Buddhist meditation has received sufficient attention. This may be because later Buddhists lost sense of the metaphor and read brahmavihāra as literally being reborn in Brahmā's world, i.e. as not leading to freedom from liberation, despite the related description cettovimutti being applied to it. My reading of the texts, following Gombrich, is that the Buddha clearly used brahmavihāra as a synonym for nibbāṇa.
So the Buddhist idea of an escape from saṃsāra was not original. What was original was how the Buddha defined 'this world' and what escaping from it meant. I have explored the former in my post What the Buddha meant by World, and clearly his definition of 'the world' as the world of experience, has profound implications for eschatology. What we are escaping from is not necessarily birth and death in the sense of physical rebirth, and physical death. Indeed the Buddha often couched his eschatological teaching in terms of escape from the experience of disappointment (dukkha). It allowed the Buddha and other arahants to say they were liberated, that they had "done what needed to be done" in their own lifetimes, without the necessity to die first (an innovation on the Brahmin conception at least!). Heaven, dwelling with Brahmā (brahmavihāra), is available here and now, according to the Buddha.
Historically Buddhists seem to have taken on existing cosmologies with some adaptation, but with a tendency to reify them for rhetorical effect. Although the Buddha defined 'this world' in terms of experience, the 'other world' became a series of actual places where one could be reborn: the brahmaloka in particular was brought within saṃsāra. This seems to have been a wrong turn, and has left us with a confused picture of cosmology and rebirth. Tradition asks us to believe quite literally in rebirth and in the various realms. The spirit in which the Buddha claimed to know Brahmā and the way to companionship with Brahmā - as a metaphor for escaping saṃsāra - has been lost. One result has been the ongoing polarisation about whether or not we Western Buddhists should believe in rebirth. On the contrary Chögyam Trungpa has spoken of the six realms as psychological metaphors rather like the Jungian archetypes, and this sits better with the idea of 'world' as experience, than more traditional realms for actual rebirth. 
One of the weird things about rebirth and karma eschatologies has been the enthusiasm for them in the West. For the Indian repeated rebirth and redeath is a curse to be escaped from. In the popular imagination of Western culture, rebirth seems an attractive proposition. We actually want to be reborn. What this tells us is that westerners in general see rebirth in terms of personal continuity. This is what the Pāli texts call 'having a pernicious view' (pāpakaṃ diṭṭḥigataṃ). When nibbāṇa is presented in terms of the end of personal continuity, I think something baulks in the Western psyche. It suggests that despite living in hedonistic and nihilistic times, that underlying this is a frustrated eternalism. Having given up on the prospect of eternal life somewhat reluctantly because of the accompanying baggage, we are drowning our sorrows. Perhaps this is also why western culture is so obsessed with youth, so mired in the Peter Pan Syndrome.
It is unlikely that Obeyesekere's book will appeal to the mass market, or even to most Buddhists. The ideas are complex, even if well presented. Complex ideas are difficult to popularise, especially in our 'sound bite' culture. However the more that we understand about how the early Buddhist presentation of the Dharma was conditioned by the time and place of its articulation, the better we will understand how to adapt it to our own times. The aspects of the Dharma that are simply cultural will stand out better, allowing us to grasp more clearly the principles which are applicable in our own context.
- Jurewicz's original paper was: Jurewicz, J. ‘Prajapati, the Fire and the pañcagnividya’. In: Balcerowicz, P., Mejor, M. (Eds.) Essays in Indian Philosophy, Religion and Literature. Delhi: Motilal Banarsidass 2004, s.45-60. A revised version of her conference paper from the 14th World Sanskrit Conference, July 2006, on this subject is on the Oxford Centre for Buddhist Studies website: Jurewicz, J. The Rigveda, 'small scale' societies and rebirth eschatology. 2006.
- KauU contains a later reworking of ideas found in BU and CU.
- I have pointed out that this idea is missing from the Pāli texts. The omission is significant, but so far not much commented upon in the academic literature. One scholar who has also noticed this is Dr Brian Black of Lancaster University, watch for a series of forthcoming publications from him.
- See Trungpa's commentary in Trungpa, Chogyam and Freemantle, Francesca (trans.). The Tibetan Book of the Dead: Great Liberation Through Hearing in the Bardo. Shambala, 1975. (link is to the new edition)
image: Monks stand waiting for a confession as a martyr is tortured on the wheel. Taken from How Stuff Works, ultimately from Hulton Archive/Getty Images.