Pange Lingua (Gregorian Chant)

According to Wikipedia: "Pange Lingua Gloriosi Corporis Mysterium is a hymn written by St Thomas Aquinas (1225–1274) for the Feast of Corpus Christi . It is also sung on Maundy Thursday, during the procession from the church to the place where the Blessed Sacrament is kept until Good Friday. The last two stanzas, called separately Tantum Ergo, are sung at Benediction of the Blessed Sacrament. The hymn expresses the doctrine of transubstantiation, in which, according to the Roman Catholic faith, the bread and wine are changed into the Body and Blood of Christ."  The beautiful Gregorian chant is performed here for Easter Mass by the Gregorian Choir of Paris.

Mozart's Ave Verum Corpus

From Thesaurus Precum Latinarum:
Ave Verum Corpus natum is a short Eucharistic hymn dating from the 14th century and attributed to Pope Innocent VI (d 1362). During the Middle Ages it was sung at the elevation of the Host during the consecration. It was also used frequently during Benediction of the Blessed Sacrament.

Praise, My Soul, The King Of Heaven

Exquisite example of English sacred music from the Choir of Westminster Abbey. "Praise, My Soul, the King of Heaven by John Goss. Words by Henry Francis Lyte (1793-1847).

Allegri's Miserere

Miserere, by Italian composer Gregorio Allegri (1582-1652), is a setting of Psalm 51 composed during the reign of Pope Urban VIII, probably during the 1630s, for use in the Sistine Chapel during matins as part of the exclusive Tenebrae service on Wednesday and Friday of Holy Week. It was extremely popular and noted for its exquisite beauty. The Vatican wanted to preserve the mystery of the piece and forbid that it be written down, threatening excommunication if anyone did. A young 14-year-old Mozart, however, being the innate genius that he was, listened to the piece as it was sung in the chapel, then wrote it down from memory later that day, words and musical scoring, in its entirety.  When it was discovered, the Pope was so impressed that he lifted the ban. (See an account of that story here)

Sacred Music: The story of Allegri's Miserere