If we were to survey American Church members, I imagine that a large segment, perhaps the majority, would indicate subscription to what I call the tripartite model of Mormon ontology. This concept is that in our most primordial existence we were sentient “intelligences” which were then transformed into spirits, typically by some form of spirit birth. Subsequently we receive a physical body destined for the resurrection. As far as I can tell, the popularity of this idea is a case study of grass roots doctrinal evolution.
Joseph Smith revealed the book of Abraham, which was published in the Nauvoo Times and Seasons. In what we now have canonized as Abraham 3, the Lord describes a cosmological hierarchy of celestial bodies and then analogizes them to individual existence. He states “[I]f there be two spirits, and one shall be more intelligent than the other, yet these two spirits, notwithstanding one is more intelligent than the other, have no beginning; they existed before, they shall have no end, they shall exist after, for they are gnolaum, or eternal.”
I am unaware of any documented reaction to this bit, but the Prophet emphasized the idea in the last months of his life in his famous “King Follett Sermon” and his June 16 “Sermon in the Grove.” In one of the best documented sections of the KFD (see here for a textual history, introduction and link to sources) Joseph Smith defiantly preached: “God never did have power to create the spirit of man at all. He could not create himself–Intelligence exists upon a selfexistent principle–is a spirit from age to age & no creation about it[.]“
Less well documented is Joseph Smith’s teachings on the concept of a Mother-God. In fact, no contemporaneous documentation is extant. That he did teach the idea is attested by reliable witnesses; what he thought it meant, not so much.
In their expansions of Mother in Heaven doctrine, Brigham Young and Orson Pratt offered competing ontologies that each abandoned Joseph Smith’s teachings on the eternality of spirit existence. Each believed in viviparous spirit birth. That is, a resurrected and glorified man and women would somehow conceive a spirit which grew in the “womb of the celestial female” to use the Prattian parlance. Young believed that spirits were formed from spirit element which was analogical to physical matter. This spirit matter was not intelligent and if a spirit merited perdition, it was recycled to create new spirits. While Young is documented to have checked-off on the “History of Joseph Smith” publication of the KFD, which included the doctrine that God could not create the spirit of man, it is not certain how or what he thought of it.
Pratt posited that each atom of spirit matter was intelligent and evolved into a higher being as it was transferred from making up variously, spirit vegetation, spirit animals and ultimately us.  Brigham Young fairly well trounced Pratt’s ideas and except for Cleon Skousen and Orson Scott Card, they haven’t really gotten much traction.
At the end of the nineteenth century and especially during the first two decades of the twentieth century, Church leaders vigorously sought to purge pioneer era doctrines that were no longer viewed as consistent with modern teachings and to systematize those modern ideas. At the forefront of this labor was B. H. Roberts. Something of a firebrand, he was extraordinarily influential and progressive in his ideas. As the editor of the History of the Church he was familiar with Joseph Smith’s teachings and he sought to alleviate the tension between Joseph’s teachings of eternal existence on one hand and Brigham Young’s spirit creationism on the other. His solution: the tripartite model.
The First Presidency thought the synthesis from Roberts dialectic was baseless, and even went so far as removing the King Follett Sermon from the History of the Church. [see discussion in n4 for details. This is one to pull out when you hear people whining about how the Church doesn't emphasize the KFD like they used to – presentist hooey.] Roberts appears to have only found support in his tripartite ideas from John Widtsoe, who tried to incorporate them in his Rational Theology, which was used as a priesthood manual. The First presidency expressed discomfort with the sections, calling them speculation, and required that they be struck before publication.
Perhaps the greatest contributor to the shift in institutional perspective regarding the KFD, and consequently spirit ontology, is Roberts’s erstwhile antagonist, Joseph Fielding Smith. Unlike his father, Joseph Fielding felt that the KFD was worth publishing and included an edited version in his very popular (and fairly historiographically flawed) Teachings of the Prophet Joseph Smith, first published in 1938 and later used as a priesthood manual.
Joseph Fielding Smith, and folks like Bruce R. McConkie and Harold B. Lee after him, basically argued for Brigham Young’s position with a change in vocabulary. While B. H. Roberts invented “intelligences” as pre-spirit beings, JFSII used “intelligence” as a synonym for Young’s spirit element. This idea is most clearly explained by McConkie in his Mormon Doctrine:
True, as Joseph Smith taught, man “is a self-existent being,” for “the intelligence of spirits is immortal,” and “had no beginning.” (Teachings, pp. 352-354.) That is to say the bodies of Deity’s spirit children were created from the existing spirit element (pg. 84)
Any notion or theory that life, or ego, or agency, existed for each individual prior to the time of the spirit birth is pure speculation, wholly unsupported by any correctly understood and properly interpreted scripture. Life began for man and for all created things at the time of their respective spirit creations. Before that there were only the spirit elements from which the Almighty would in due course create life. (pg. 442)
This spirit element has always existed; it is co-eternal with God. (Teachings, pp. 352-354.) It is also called intelligence or the light of truth, which “was not created or made, neither indeed can be.” (D&C 93:29)
Speaking of pre-existent spirits, Abraham calls them “the intelligences that were organized before the world was.” (Abra. 3:22-24.) Thus, portions of the self-existent spirit element are born as spirit children, or in other words the intelligence which cannot be created or made, because it is self-existent, is organized into intelligences. (pg. 751)
As far as I can tell, the tripartite model has been publicly, though rarely, taught by a few living general authorities; but it is Truman Madsen, student and biographer of B. H. Roberts, that has been the most vocal proponent (surely to the consternation of Joseph Fielding McConkie).