It's not "strange" at all. Watch "Dead Again," a Kenneth Brannagh film. I loved that reincarnation story.
Cloud Atlas and The Fountain were a bit "out there" for me, to be honest.
I am currently shopping a short speculative story that I've written where it's been proven (scientifically) that we have souls and that they do reincarnate and mankind has learned how to "tag" souls. So, you are born and "scanned" and everyone knows who you were in a past life. My piece takes place in a boy's "home" where they send children who have been awful people in past incarnations (e.g. murderers and such).
I've read a few SFF pieces that delve into this in a less "ethereal" way than something like Cloud Atlas or The Fountain.
From what I've read, it's both spiritual and cultural. The whole East Indian caste system is kind of built around that, no? Someone here will probably have better articulation of this. You're born into a certain caste and there you must stay because that's what position you were born into. If you're good and pay your dues, you might be born further up the ole social ladder next time. I believe that Hindus, for example, don't believe in conversion because even if you are the lowliest of Hindus (untouchables in India, for example), at least you were born into the religion and are special because of that. Modern "takes" obviously overlook this: hari krishnas, etc.
Ian Stevenson had some pretty interesting research going on about reincarnation. I read it quite a while ago. It's where I got the idea for my story. He investigated cases where children remembered past lives and tried to find the families of those children, etc.
http://www.near-death.com/experiences/reincarnation01.html
I'm not saying his work is infallible, but it's interesting to read.