Taking a look at each person called to the First Presidency or Quorum of the Twelve by each prophet. Joseph Smith had the most, naturally, so I'm dividing him into two posts. First, I'll cover the eleven men he called as apostles or counselors that were never part of the Quorum of the Twelve.
(Oct 3, 1806 - March 3, 1850)
Apostle - 1829
Assistant President - 1834
Excommunicated - 1838
Rebaptized - 1848
Oliver Cowdery was there in the beginnings of the Church. He met Joseph Smith in 1829 and became one of his chief scribes in the translation of the Book of Mormon. He was one of the Three Witnesses who was shown the plates by an angel. He was given the Aaronic Priesthood with Smith by John the Baptist, and later he was given the Melchizedek Priesthood with Smith by Peter, James and John. When the LDS Church was organized in 1830 with six people, Smith was named First Elder, and Cowdery was Second Elder. Had he stayed with the Church through 1844, he likely would have been its next prophet.
The collapse of the Kirtland Safety Society disillusioned him and many other Saints. He also vehemently disagreed with polygamy, and when a church court called him to excommunicate him, he resigned his membership instead.
After Smith's death, he looked into the claims of James J. Strang to be the next leader of the Church, and even moved to Wisconsin in 1847 where Strang's followers gathered. But by 1848, he wanted to reunite with The Church of Jesus Christ of Latter-day Saints led by Brigham Young. He was rebaptized a few months later, and although he desired to join the Saints in Utah, his poor health prevented it. He died from tuberculosis in 1850 at only 43 years old.
(January 7, 1805 - January 25, 1888)
Apostle - 1829
Resigned his membership - 1838
Whitmer had many of the same experiences as Cowdery early in the Church. He was with Smith and Cowdery when the angel appeared to them and showed them the golden plates, and as such he became one of the Three Witnesses. There was a period in 1834 where he was second in line for president of the Church until Cowdery was made Assistant President. He, Cowdery and Martin Harris were in charge of selecting the first twelve members of the Quorum of the Twelve Apostles.
His disaffectation with Smith happened around the same time as Cowdery's and for most of the same reasons. He resigned his own membership shortly before Cowdery's excommunication court.
In 1844, he briefly started his own church but it quickly fizzled. Cowdery encouraged Whitmer to give the LDS church another chance, but Cowdery died before their correspondence went anywhere. Whitmer tried reviving his own church in 1876, and it lasted for a while but the last member of his spinoff died in 1961.
(May 18, 1783 - July 10, 1875)
Apostle - (unclear when he was ordained)
Excommunicated - 1837
Rebaptized - 1870
The third of the Three Witnesses, though Harris had his own vision and meeting with the angel later that day from Cowdery and Whitmer. He'd been an early scribe for the translating of the Book of Mormon, writing 116 pages' worth that Harris then lost. Smith used others to finish the work.
In 1837, after the failure of the Kirtland Safety Society, Harris and some other reformers called Smith a fallen prophet and "excommunicated" him. Smith turned around and excommunicated them instead.
After Smith's death, Harris looked to join the Strangite movement. By 1847, he split with them and tried joining Whitmer's short-lived spin-off. He also followed Joseph's brother William as a prophet in 1855. He gave the Shakers a try. He would pursue each alternative zealously, but then would quickly burn out.
By 1870, he was ready to rejoin the LDS Church. He made his way to Utah, was rebaptized, and lived out the rest of his days in Utah.
(1785 - c.1836)
First Counselor - 1832
Excommunicated - 1832
Not much is known about him. He'd only been a member a few months when he made First Counselor, and not much is known about why he left the Church. He was lost to church history for over a century.
(February 19, 1793 - July 14, 1876)
Second Counselor - 1832
First Counselor - 1833
Excommunicated - 1844
Rigdon was one of Smith's closest allies, and yet there were pockets of estrangement, especially toward the end of Smith's life. Rigdon began edging out Cowdery as the second-in-command once he became First Counselor, even though Cowdery was Assistant President. Rigdon and Smith also had a vision together where they saw Christ.
After the Kirtland Safety Society fell apart and many leaders left the church, Rigdon stayed loyal and gained more trust with Smith. In 1841, Smith ordained him as a Prophet, Seer and Revelator. By 1843, though, he wanted Rigdon removed as his Counselor. The body of the church rejected this, and so Rigdon stayed on. When Smith last met with the Quorum of the Twelve, he reaffirmed to them they were Prophets, Seers and Revelators, with all the keys of the Priesthood he had. When Smith died, Rigdon instantly asserted himself as the logical successor, and the senior-ranking counselor in the First Presidency. He also said he received revelation he should be the Guardian of the Church. Brigham Young, President of the Twelve, argued the Apostles should lead the church, and the majority of the church sided with Young, including Amasa Lyman and John Smith, the other surviving counselors in the First Presidency.
The Presiding Bishop, Newel K. Whitney, excommunicated Rigdon in September 1844, and Rigdon turned around and excommunicated the Twelve. He started his own church, which fizzled out by 1847 until William Bickerton reorganized it as The Church of Jesus Christ in 1862. It still has about 12,000 members today.
FREDERICK G. WILLIAMS
(October 28, 1787 - October 10, 1842)
Second Counselor - 1833
Removed by Church vote - 1837
Excommunicated - 1839
Rebaptized - 1840
Williams had been a member of Rigdon's Baptist congregation when he, Rigdon and other future church leaders were converted and baptized. He joined the First presidency in 1833, but after the collapse of the Kirtland Safety Society, the majority of the church refused to sustain him. While Joseph Smith was in Liberty Jail, he excommunicated Williams, but he fully restored him a few months later. Williams died at age 54.
(February 9, 1800 - June 27, 1844)
Second Counselor - 1837
Apostle - 1841
Assistant President - 1841
Killed - 1844
Joseph's older brother, as well as his uncle and father, were made additional counselors in 1837, but within two months, Hyrum's title was changed to 2nd Counselor. Hyrum was given the office of Apostle as well as Assistant President in 1841, and had he not been killed the same day as Joseph, there's no question he would have been sustained as the next prophet.
(July 16, 1781 - May 23, 1854)
Assistant Counselor - 1837
Joseph's uncle was the father of George A. Smith, called to be an Apostle in 1839. John served in the First Presidency through Joseph's death, then sided with Brigham Young and joined the Saints out west. He became the Presiding Patriarch of the church in 1849, and held that office until his death at age 72.
JOSEPH SMITH SR.
(July 12, 1771 - September 14, 1840)
Assistant Counselor - 1837
Joseph Smith's father was a loyal counselor and one of the Eight Witnesses to the Book of Mormon (as was Hyrum). He died of illness at age 69.
JOHN C. BENNETT
(August 3, 1804 - August 5, 1867)
Assistant President - 1841
Excommunicated - 1842
Bennett entered Smith's circle of trust quickly and became the mayor of Nauvoo and general in the Nauvoo legion, in addition to his church leadership. As the second assistant president, he could have claimed third-in-command of the whole church, depending how one would interpret his calling. But by 1842, tales of adultery, homosexuality and abortions brought him down, and he was excommunicated. After that, he became a bitter enemy of the church and vowed to drink Smith's blood. He traveled the country preaching against them. After Smith was killed, he tried joining Sidney Rigdon's spinoff, and then the Strangite crowd, but he was kicked out for sexual misconduct, and that was that.
(September 8, 1809 - January 19, 1892)
Second Counselor - 1841
Excommunicated - 1844
Law was baptized in 1836, and he helped convert many Canadians and brought them to Nauvoo. He was made second counselor after Hyrum was elevated to Assistant President in 1841. Law grew increasingly uncomfortable with the doctrine of polygamy and began to view Smith as a fallen prophet. He was removed from the First Presidency in January 1844 and finally excommunicated in April. He turned around and started the Nauvoo Expositor, a paper dedicated to bring down Joseph Smith. After one issue, the Nauvoo City Council ordered the Nauvoo Expositor press destroyed, which the militia carried out later that day. Joseph & Hyrum Smith were arrested in relation to the destruction of the press, and it was while they were being held that a mob stormed the jail and murdered them.
Law started his own church, with himself as president (not prophet), but that dwindled into obscurity fairly quickly. He continued to slam Smith and the LDS church the remainder of his days.
I think what this shows, the history of who he called, was that Joseph Smith was a very trusting person. That trust wound up getting betrayed, even as many of his followers felt betrayed by him. It's amazing the church survived at all.
[Side note: Looking up some old Salt Lake Tribune articles for this, I was floored at just how virulently anti-Mormon the Trib used to be. Upon Brigham Young's death, they denounced him as "Satanic".]