Here is a Bach (and Handel) favorite for all miserere nostri.
By Palestrina:
http://www.youtube.com/watch?v=2z3M1...eature=related
By Gr.Allegri
http://www.youtube.com/watch?v=Cn39RzlhSao
WIKIquote:
According to the popular story (backed up by family letters), the fourteen-year-old Mozart was visiting Rome, when he first heard the piece during the Wednesday service. Later that day, he wrote it down entirely from memory, returning to the Chapel that Friday to make minor corrections. Some time during his travels, he met the British historian Dr Charles Burney, who obtained the piece from him and took it to London, where it was published in 1771. Once the piece was published, the ban was lifted; Mozart was summoned to Rome by the Pope, only instead of excommunicating the boy, the Pope showered praises on him for his feat of musical genius[citation needed]. The work was also transcribed by Felix Mendelssohn in 1831 and Franz Liszt, and various other 18th and 19th century sources survive. Since the lifting of the ban, Allegri's Miserere has become one of the most popular a cappella choral works now performed[who?].
JS Bach of course, earlier on, "borrowed" from Palestrina (JS's Mass in B minor).
One can but assume he obtained the work thru his "son", "Johann Christian Bach" aka "Phantom of the opera".