The Hymn Nearer My God to Thee has often been suggested as the last tune played by the Musicians on the Titanic.
There are different versions of the hymn, all are set to verses, written in 1841, by the English poet Sarah Fuller Flower Adams (1805-48) (1). An English version is set to the tune Horbury composed in 1861 by John Bacchus Dykes (1823-1876). Methodists use the accompaniment Propior Deo composed by Sir Arthur Seymour Sullivan (1842-1900), while an American version is sung to the tune Bethany (written in 1859) (2) by Lowell Mason (1792-1872).
1. Nearer, my God to Thee,
2. Though like the wanderer,
3. There let my way appear
4. Then with my waking thoughts
5. Or if on joyful wing,
6. There in my Father's home,
1. Verses 1-5 are by Adams, an additional verse 6 was written by Edward Henry Bickersteth, Jr.
2. Another source says 1856.
Horbury (Dykes) (Instrumental midi) (1912 Recording wav)
Propior Deo (Sullivan) (midi)
Bethany (Mason) (Instrumental midi) (1999 Recording wav from 'Be British!' - and Other Classic Titanic Songs courtesy Johan Tötterström).
The Oxford Dictionary of Music
Walter Lord (1986) The Night Lives On: Thoughts, Theories and Revelations about the Titanic. London, Penguin. ISBN 0 140 27900 8
The Cyber Hymnal (http://www.cyberhymnal.org/)