One might invent a science-fictional rationale for reincarnation, perhaps using the concept of a physical stream of particles such as the "mindons" of Bob Shaw's Orbitsville Departure. However, what most people mean by reincarnation - the soul, which is to say the qualitative aspect of a person, living consecutive lives in different bodies - is not regarded as a scientific concept by most people, and sits uneasily in a science fiction story.
Various ways have been tried of getting some of the benefits of reincarnation by means of other plot devices. The serial bodies of van Vogt's hero Gosseyn in The World of Null-A and of the immortal citizens in Jack Vance's To Live Forever; the matter-transmitting duplicates in Algis Budrys's Rogue Moon - these are not precisely reincarnation but they do give the hero a chance to live again after he is killed.
In Robert Heinlein's Beyond This Horizon a scientific investigation reveals that reincarnation does happen; it is announced as a discovery, albeit an unexplained one. In Edgar Rice Burroughs' The Moon Maid the existence of reincarnation is accepted unquestioningly by the people of the Moon, and is experienced by the terrestrial narrator.
Obviously the concept offers enormous benefits to any storyteller who wants plots full of vistas of time and opportunity. There is perhaps a danger of it becoming too open-ended, in that if a serial infinity of lives is on offer, the urgency of any one life may seem diminished. In so far as that may be a problem, it is dealt with in the variation on the reincarnation theme provided by the Ooranye Project. On the giant planet the inhabitants take for granted the fact that they will have more than one life, but they also know that the number of their lives is limited, to two or, in rare cases, three. After that, their soul's destiny is unknown to them.
In William Hope Hodgson's The Night Land it is suggested that lovers parted by tragedy in one life may meet in another, but on Ooranye there is no mystical affinity to help this process along, and indeed, in "The Open Secret" the rare statistical chance which does enable such a couple to meet again, leads to fear as well as joy.
