The Essentials

(In Progress)
Like any list or ranking, there will always be a subjective element involved. However, after consulting numerous lists of this type, looking at the literature, and using my personal expertise (Music History and Literature degree after all), a fairly decent list can be arrived at.
Full Disclosure: Since the defense of the Judeo-Christian and classical (Greco-Roman) heritage is the primary purpose of this site, it will be abundantly clear to the discerning reader that the western music that reflects this will take priority, and the departure from this heritage that started in the 19th century and later requires more “stinginess” if you will.

Essential Works for Western Music Literacy (recommended recordings will be added as time permits).

Bach, Johann Sebastian (1685-1750)
Brandenburg Concertos 1-6
Orchestral Suites (Overtures) 1-4
Mass in Bminor
St. Matthew Passion
Organ Works, especially the Toccata and Fugue in Dminor, Chorale Preludes, and the Passacaglia and Fugue in Cminor
Italian Concerto
The Well-Tempered Clavier

Beethoven, Ludwig van (1770-1827)
Symphonies 1-9. Good sets can also be found here, here, here, and here.
Piano Concerti 1-5.Two other good sets can be found here and here.
Piano Sonatas. There are 32, so there are some discs which have only the most famous which are readily available.
String Quartets
Missa Solemnis
Violin Concerto

Brahms, Johannes (1833-1897)
Symphonies 1-4
Piano Concertos 1-2
A German Requiem
Violin Concerto
Piano Quintet
Horn Trio
Solo Piano Music (especially Variations on a Theme of Handel, Op.79 Rhapsodies)
Clarinet Quintet

Corelli, Arcangelo (1653-1713)
Concerti Grossi. Bargain set of Corelli’s complete works can be found here.

Couperin, Francois (1668-1733)
Ordres for Harpsichord

Dvořák, Antonín (1841-1904)
Symphonies, especially 7-9.
Humoresques
Cello Concerto
“Dumky” Trio

Gabrieli, Giovanni (C1554/1557-1612)
Sonatas and Canzoni for Brass

Handel, George Frederic (1685-1759)
Concerti Grossi
Messiah. Recordings here and here are also quite good in lieu of the Pinnock.
Israel in Egypt
Solomon
Royal Fireworks Music
Water Music
Julius Caesar (Gulio Cesare)

Haydn, Franz Joseph (1732-1809)
Symphonies (Over 100 of them, but especially the 12 London Symphonies, 6 Paris Symphonies, and the “Farewell“
The Creation
Trumpet Concerto
String Quartets, especially Op.71, 74, 76, and 77

Josquin des Prez (c.1450-1521)
Motets/Chansons
L’Homme Arme Masses

Leonin (c.1150-1201?)
Magnus Liber (Sacred Organum)

Machaut (c.1300-1377)
Sacred Music (Motets, Masses, etc…)

Mendelssohn, Felix (1809-1847)
Symphonies 3-5
Violin Concerto
Elijah
Music for A Midsummer Night’s Dream

Monteverdi, Claudio (1567-1643)
L’Orfeo
Madrigals
Vespers

Mozart, Wolfgang Amadeus (1756-1791)
Piano Concerti, especially 10, 19-27
Symphonies, in particular 25, 29, 35-41
Don Giovanni
The Marriage of Figaro
Requiem
Eine Kleine Nachtmusik (Serenade no.13)
Posthorn Serenade
Horn Concertos 1-4
Clarinet Quintet
Clarinet Concerto

Ockeghem, Johannes (C1420-1497)
Missa Prolationum

Perotin (c.1200)
Sacred Music (organum)

Praetorius, Michael (1571-1621)
Terpischore
Sacred Music

Purcell, Henry (1659?-1695)
Anthems
Dido and Aeneas
Fantasias/Fantasies

Rameau, Jean Philippe (1683-1764)
Pieces de Clavecin
Ballet Music

Rossini, Gioachino (1792-1868)
The Barber of Seville
William Tell

Scarlatti, Domenico (1685-1757)
Sonatas for Keyboard

Schubert, Franz (1797-1828)
Symphonies, 5,8,9
Lieder (Songs), there are over 600, but the cylces Die Winterreise (Winter Journey) and Die schöne Müllerin are a good start
Trout Quintet
Mass in Eflat

Schumann, Robert (1810-1856)
Symphonies, 1-4
Piano Concerto
Carnaval
Kinderscenen
Piano Quintet

Schütz, Heinrich (1585-1672)
Sacred Works (Psalms of David, St. Matthew Passion, Symphoniae Sacrae)

Telemann, Georg Philipp (1681-1767)
Tafelmusik (Musique de Table, Table Music)
Orchestral Suites

Vivaldi, Antonio (1678-1741)
The Four Seasons
Concertos (for virtually all instruments available during his day)
Gloria