They shall have stars at elbow and foot;
Though they go mad they shall be sane
Though they sink through the sea they shall rise again;
Though lovers be lost love shall not...
And death shall have no dominion.
~ Dylan Thomas
Offering prayers for the well being of the beloved dead is a custom in nearly every religion. Many religions also encourage prayers for the unknown dead, usually those who share our own faith, but sometimes for all those who have passed on. Rosaries and chaplets are often used to track these prayers.
In the Roman Catholic church a rich tradition of prayers said specifically for the souls of those in purgatory has developed through the centuries.
There is evidence of the custom of praying for the dead in the inscriptions of the catacombs, with their constant prayers for the peace and refreshment of the souls of the departed, and in the early liturgies, which commonly contain commemorations of the dead.
Beginning as early as 336 with the Brotherhood of Constantinople and continuing with the early religious orders, special association were created for the purpose of praying for the comfort and uplifting of the souls of the dead. First consisting only of members of religious orders, by the 9th century these association consisted mostly of laymen under the supervision of a bishop. Some of the medieval confraternities exist to this day; The Confraternity of Our Lady of Suffrage (Santa Maria del Suffragio) has existed in Rome since 1592.
At Nīmes, a confraternity similar to that of Our Lady of Suffrage was established under the same name in 1857, received the faculty of aggregating other confraternities in the Diocese in 1858, and in 1873 received the same right for the world. In addition to the indulgences of the Roman confraternity, that of Nīmes has received others: the recital of the Rosary of the Dead was approved especially for its members by Pius IX in 1873. 
The idea of a special chaplet that would be used just for these prayers is sometimes credited to Archbishop Plantier, Bishop of Nimes, or alternatively to Abbé Serre of the Chapel of the Hōtel Dieu at Nimes.
It is this rosary that we usually mean when we say "The" rosary for the dead; four decades with 3 spacer beads, a drop of one bead, and a crucifix. Often, a medal of Notre Dame du Suffrage is attached with the crucifix. This design is the one approved and blessed by Pope Pius IX in 1873. More recent versions may have a drop of five beads. This appears to be a variation, not a error, as Beads for the Dead created early in the 20th century at the sanctuary in Nimes sometimes include a five bead drop.
Beads for the Dead were produced and issued by the Archconfraternity from the late 19th through the mid 20th centuries. The archconfraternity's house in Nimes, France appears to still be in operation: http://nimes.catholique.fr/partenaire/mouvement/v_mv_pr.php?ID=62
Eternal rest grant unto him/her (them), O Lord; and let perpetual light shine upon him/her (them).
May he/she (they) rest in peace.
We give Thee thanks for all Thy benefits, O Almighty God, Who livest and reignest forever.
And may the souls of the faithful departed, through the mercy of God, rest in peace.
The Penitential Psalms -- Psalms 6, 31, 37, 50, 101, 129, 142 -- are also prayed for the dead, especially the 129th Psalm, known as De Profundis (Out of the Depths):
Out of the depths have I cried unto Thee, O Lord: Lord hear my voice.
Let Thine ears be attentive to the voice of my supplication.
If Thou, Lord, shouldst mark iniquities, O Lord, who shall stand?
But there is forgiveness with Thee: because of Thy law I wait for Thee, O Lord.
My soul waiteth on His word: my soul hopeth in the Lord.
From the morning watch even until night let Israel hope in the Lord: For with the Lord there is mercy, and with Him is plentiful redemption.
And He shall redeem Israel, from all their iniquities.
Université du Littoral, Grand-rue, 62327 Boulogne-sur-Mer. (http://www.oxfordjournals.org/)
The cult of souls in purgatory underwent a massive revival in France during the second half of the nineteenth century and recorded, at least down to the Great War, a success that made a stunning contemporary impact. The importance of the cult of the dead, the hopes and fears it aroused among the clergy, the necessity of striking an expiatory balance between the decline of belief in Hell and the hope of going to Heaven, plus the desire to counteract those developments that called into question the Catholic belief in last things, all help to explain the phenomenon. The nineteenth-century movement, which was situated in the context of a long history of belief in purgatory, was endowed with specific features, on the doctrinal as well as on the devotional and institutional levels. The two most significant innovations were prayers for abandoned souls, and the recourse to souls in purgatory as intercessors for the living. In welcoming the advent of this thaumaturgical dimension, which had hitherto been lacking, the cult was provided with a solid foundation, which turned the nineteenth century into the age par excellence of the cult of souls in Purgatory.
At Nīmes, a confraternity similar to that of Our Lady of Suffrage was established in 1857, received the faculty of aggregating other confraternities in the Diocese in 1858, and in 1873 received the same right for the world. In addition to the indulgences of the Roman confraternity, that of Nīmes has received others: the recital of the Rosary of the Dead was approved especially for its members by Pius IX in 1873.
In accordance with its ancient traditions, the Benedictine order formed a twofold Confraternity of the Poor Souls at Lambach, Austria. In 1877 the Archconfraternity of the Perpetual Adoration of the Blessed Sacrament under the protection of St. Benedict for the Poor Souls in Purgatory was erected with the right to aggregate other confraternities of the same name and object in Austrohungaria. In 1893, this confraternity was erected in the abbey church of St. John the Baptist in Collegeville, Minnesota; it shares in all the indulgences of the Lambach confraternity, and possesses, as the archconfraternity of North America, the faculty of aggregating all confraternities of the same name and communicating to them its indulgences. Finally, by 1910, Pius X granted to Lambach Confraternity the right to aggregation for the whole world. There was also founded, in 1878, in the same abbey church of Lambach a Priest's Association under the Protection of St. Benedict for the Relief of the Poor Souls in Purgatory. This was approved and recommended by the diocesan bishop, Franz Joseph Rudigier. Many other bishops, especially in North America, recommended it to their clergy. The direction of the association was placed in the hands of the general director of the Archconfraternity of Lambach, who entered the members in a special register. The official organ for both was the "Benediktusstimmen" published by the Abbey of Emaus in Prague.
The Order of Cluny have always been conspicuous for their devotion to the poor souls. Since 998, St. Odilio, Abbott of Cluny, had All Soul's Day celebrated by his monks on 2 November, which day was gradually devoted by the entire church to the relief of the poor souls. In memory of this fact, a new archconfraternity was erected at Cluny in the parish of Our Lady. By Brief of 25 May, 1898, Leo XIII granted this "Archconfraternity of Prayer for the Poor Souls in Purgatory" the indulgences of the old Roman Confraternity of Prayer and Death (see above), and authorized it to aggregate similar confraternities throughout France and its colonies. The "Associazione del Scaro Cuore di Gesū in suffrago della Anime del Pugatorio" was canonically established in Rome (Lungotevere, Prati), in a church of the Sacred Heart, and granted indulgences and privileges by Leo XIII (1903-5). The director of this association, which includes non-residents of Rome in its membership, edits "Rivista mensile dell' Associazione".
The formation of the "Catholic League for Constant Intercession for the Poor Souls in Purgatory" was proposed by certain pious citizens of Rome, approved by Leo XIII in the last years of his reign, and enriched with indulgences. The only requisite for membership is to recite thrice daily the prayer, "Requiem ęternam dona eis Domine et lux perpetua luceat eis. Requiescant in pace. Amen", thereby gaining once daily an indulgence of 200 days.
Purgatorial Societies http://www.newadvent.org/cathen/12572a.htm
1) Oxford Dictionary of the Christian Church, Oxford University Press (2005)
2) Michael, "Gesch. des deutschen Volkes", I (1897)
3) Beringer, "Die Ablässe", II, 3rd ed.