Origin of Mormon Prayer Circles
Ritual prayer in a circle around an altar is not unique to Mormonism or even Christianity. Ritual ceremonies around an altar are common in paganism, and ritual prayer dances around an altar were practiced by early Christians, especially Gnostics, before the practice was condemned as a heresy by the Second Council of Nicaea in 787 A.D. See Nibley, "The Early Christian Prayer Circle" at 41. Much later, Protestants began conducting informal prayer circles.
Prayer circles were common in the Protestant revivals of the Second Great Awakening that occurred in the youth of Joseph Smith, Jr Ritual circles were also practiced in Freemasonry, to which Smith had been initiated in 1842. Early Mormons practiced conventional Protestant-type prayer circles at least as early as 1833.
On May 4, 1842, Joseph Smith met with nine other men and performed the first Ceremony. It is not clear whether this ceremony included a prayer circle. However, prayer circles became the main purpose of meetings of the Anointed Quorum on May 26, 1843. Women were first included in the ceremony on Sept. 28, 1843. See D. Michael Quinn, "Latter-day Saint Prayer Circles" at 84.
Prayer Circles in the Church of Jesus Christ of Latter-day Saints
After the death of Joseph Smith, Jr, the Church of Jesus Christ of Latter-day Saints continued to practice prayer circles in Latter-day Saint temples. In addition, local stake and ward prayer circles were organized and conducted until May 3, 1978, when the First Presidency announced that all prayer circles should be discontinued except those performed in a temple as part of an Endowment ceremony. See Spencer W. Kimball, N. Eldon Tanner, and Marion G. Romney, Letter to All Stake Presidents and Bishops, May 3, 1978; "Update", 3 Sunstone 6 (July-August 1978). The reason for this change is unknown, but could have resulted in part from the explosive growth of the Church, and the fact that prayer circles were usually organized by a member of the First Presidency or the Quorum of the Twelve Apostles. See Quinn, "Latter-day Saint Prayer Circles" at 105. Others have speculated that the change stems from the desire of the Latter-day Saint leadership to more tightly control the use of the associated "priesthood keys" and spiritual gifts to prevent misuse of God's power and gifts.
Similar to the speaking of tongues in local meetings, the practice largely died out by the mid-1920s (today in the Church the gift of tongues is rarely used to speak in the Adamic language, and instead, is primarily used by missionaries in learning a second or foreign language).