Hinduism: The body dies, assert Hindu traditions, but not the soul, which they assume to be the eternal reality, indestructible and bliss :
Japanese Zen: reincarnation is accepted by some, but rejected by others.
A distinction can be drawn between "folk Zen", as in the Zen practiced by devotional lay people, and "philosophical Zen".
Folk Zen generally accepts the various supernatural elements of Buddhism such as rebirth.
Philosophical Zen, however, places more emphasis on the present moment 
μετεμψύχωσις - metempsychosis
εμπψχωύν - empsykhoun
παλιγγενεσία - palingenesia
גלגול הנשמות - gilgul neshamot
पुनर्जन्मन् - punarjanman
REINCARNATION IN ASIA:
4. H. Y. Ginsburgh, "Tav: Impression - The Seal of Creation," [Online]. Available: www.inner.org/hebleter/tav.htm.
12. Sefer HaGilgulim, "The Book of Reincarnations," by Chaim Vital
Punarjanman: (Sanskrit: पुनर्जन्मन्) means "rebirth, transmigration" 
Sautrantika: Some schools conclude that karma continues to exist and adhere to the person until it works out its consequences. For the Sautrantika school, each act "perfumes" the individual or "plants a seed" that later germinates 
Sikhism: teaches a doctrine of reincarnation based on the Hindu view but in addition holds that, after the Last Judgment, souls—which have been reincarnated in several existences—will be absorbed in God 
Tibetan Buddhism: stresses state of mind at the time of death. To die with a peaceful mind will stimulate a virtuous seed and a fortunate rebirth; a disturbed mind will stimulate a non-virtuous seed and an unfortunate rebirth :
Taoism: Documents from as early as the Han Dynasty claimed that Lao Tzu appeared on earth as different persons in different times beginning in the legendary era of Three Sovereigns and Five Emperors. The (ca. 3rd century BC) Chuang Tzu states: "Birth is not a beginning; death is not an end. There is existence without limitation; there is continuity without a starting-point. Existence without limitation is Space. Continuity without a starting point is Time. There is birth, there is death, there is issuing forth, there is entering in" .
Buddhism: According to various Buddhist scriptures, Gautama Buddha believed in the existence of an afterlife in another world and in reincarnation :
Jainism: 17th century cloth painting depicting seven levels of Jain hell according to Jain cosmology. Left panel depicts the demi-god and his animal vehicle presiding over the each hell :