In the July 29 2005 edition of The Salt Lake Tribune, there is an article on reincarnation in the theology of The Church of Jesus Christ of Latter-day Saints, also known as LDS or Mormonism. Very interesting reading - not an official belief, but it certainly reveals their heritage. It can be found here in the archives of ReligionNewsBlog.com
A few noteworthy quotes:
[W]ouldn't Smith know if reincarnation was central to his own revelations? Not necessarily, says Beckstead, quoting Brigham Young University anthropologist John Clark, who "suggested in a recent symposium at the Smithsonian Library that Joseph Smith was the translator, not the author, of the Book of Mormon, and consequently 'did not fully understand' its contents." ...
In April 1843, for example, Smith taught that "the purpose of successive probations or 'worlds' was to permit the gradual accumulation of intelligence and knowledge," Beckstead says. ...
"Mary Elizabeth Rollins, who wed Joseph in February 1842, claimed that he suggested to her they had an intimate relationship before they met," Beckstead says. ...
LDS apostle Bruce R. McConkie attacked reincarnation theology more directly, ridiculing the idea of plural probations. "There is no such thing as a second chance to gain salvation," he said in a 1980 church address titled "The Seven Deadly Heresies." "This life is the time and the day of our probation. After this day of life, which is given us to prepare for eternity, then cometh the night of darkness wherein there can be no labor performed."

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