A litany is a form of prayer used in church services and processions that consists of a number of petitions. The word comes from the Latin litania and the Ancient Greek: ???????? (litaneía), which in turn comes from Ancient Greek: ???? (litê), meaning “supplication”.

The frequent repetition of the Kyrie was probably the original form of the Litany, and was in use in Asia and in Rome at a very early date. The Council of Vaison in 529 passed the decree: “Let that beautiful custom of all the provinces of the East and of Italy be kept up, viz., that of singing with great effect and compunction the “Kyrie Eleison” at Mass, Matins, and Vespers, because so sweet and pleasing a chant, even though continued day and night without interruption, could never produce disgust or weariness”.

Source: Wikipedia, with adaptations

There are many litanies in use today. One common one is the LItany of Loreto, a series of petitions to Our Lady under many different titles. Here it is: 

V. Lord, have mercy.
R. Christ have mercy.
V. Lord have mercy.

Christ hear us.
R. Christ graciously hear us.

God the Father of heaven, have mercy on us.
God the Son, Redeemer of the world, have mercy on us.

God the Holy Spirit, have mercy on us. 
Holy Trinity, one God, have mercy on us.

Holy Mary, pray for us. 
Holy Mother of God, pray for us. 
Holy Virgin of Virgins, [etc.]
Mother of Christ,
Mother of divine grace,
Mother most pure,
Mother most chaste,
Mother inviolate,
Mother undefiled,
Mother most amiable,
Mother most admirable,
Mother of good Counsel,
Mother of our Creator,
Mother of our Saviour,
Virgin most prudent,
Virgin most venerable,
Virgin most renowned,
Virgin most powerful,
Virgin most merciful,
Virgin most faithful,
Mirror of justice,
Seat of wisdom,
Cause of our joy,
Spiritual vessel,
Vessel of honor,
Singular vessel of devotion,
Mystical rose,
Tower of David,
Tower of ivory,
House of gold,
Ark of the covenant,
Gate of heaven,
Morning star,
Health of the sick,
Refuge of sinners,
Comforter of the afflicted,
Help of Christians,
Queen of Angels,
Queen of Patriarchs,
Queen of Prophets,
Queen of Apostles,
Queen of Martyrs,
Queen of Confessors,
Queen of Virgins,
Queen of all Saints,
Queen conceived without original sin,
Queen assumed into heaven,
Queen of the most holy Rosary,
Queen of peace,

V. Lamb of God, Who takest away the sins of the world,
R. Spare us, O Lord. 

V. Lamb of God, Who takest away the sins of the world,
R. Graciously hear us, O Lord. 

V. Lamb of God, Who takest away the sins of the world,
R. Have mercy on us.

V. Pray for us, O holy Mother of God.
R. That we may be made worthy of the promises of Christ.

Let us pray. Grant, we beseech Thee, O Lord God, that we thy servants may enjoy perpetual health of mind and body, and by the glorious intercession of blessed Mary, ever Virgin, may we be freed from present sorrow, and rejoice in eternal happiness. Through Christ our Lord. R. Amen.