I've skewed mine slightly to bring a little more genre diversity to the list. However all of these albums are not only personal favourites but also, in my opinion, perfect or near-perfect musical statements. Two of them are live albums:
Louis Armstrong: Plays W.C. Handy
Same Cooke: One Night Stand - Live at the Harlem Square Club
The Miles Davis Quintet: 'Round About Midnight
Edward Elgar: Cello Concerto (performed by Jacqueline du Pre, with the London Symphony Orchestra conducted by Sir John Barbirolli
The Bill Evans Trio: Waltz for Debby
The Go-Betweens: Tallulah
Charles Mingus: Mingus Ah Um
Dolly Parton: The Grass is Blue
The Sundays: Reading, Writing and Arithmetic
The Waterboys: Fisherman's Blues