I can see Qwerty's point here. Eastern religions introduced the concept to the west (and a lot longer ago, with much more influence on the development of "western" religion, than most people realize), but today the concept is pervasive and not always directly or visibly tied to those eastern sources.
- New Age beliefs in "remembering one's past lives" takes reincarnation completely for granted. That there is little connection with real eastern beliefs is demonstrated by how many New Agers claim to have been Cleopatra in a past life -- which by the Dharmic traditions I'm familiar with, would imply that they'd lived very poorly since then. Having been a slave or a rat 40 past-lives ago would do them more credit.
- Speaking of rats, there appears to be a reincarnation-believing subculture among furries, as one possible explanation of the nature and origin of their animal identities.
- Native American and Inuit traditions include reincarnation, which must therefore have either developed independently or had a common origin with Asian traditions well before recorded history.
- 19th-century spiritism adopted reincarnation with little else of the eastern traditions. From there it seems to have become a standard element in the pop-culture envelope of "magic" in general. Thus, for instance, in TV series in which "magic is real," reincarnation tends to come in by default among other things that are assumed to be "also real if magic is real," such as astrology, psychic powers, love potions, vampires, and familiars.