There have been scores of reincarnation stories that pointed to lower economic straits in an earlier lifetime. And there are well-known mechanisms for people wanting to prefer more desirable identities )or more powerful ones) than those they actually remember.

But that is not alternate or parallel worlds. I think some of the tales told by "abductees" smack of bleed-through between universes (if not hyperspace travel) but of course these are not my own experiences.