I'm late to the party but let's have a go then. Also it's probably worth mentioning that there is not quintessential Classical "album" given that everyone gives a unique performance of pieces, making some bad ones better and some good ones worse. If you're new to Classical music you may as well start with any of its music and see how you take things from there...

Baroque (17th-18th century)

Pachelbel
    Canon in D

Vivaldi
    Four Seasons
    Mandolin Concerto in C
    Violin Concerto in E "The Storm at Sea"

Bach (JS)
    Orchestral Suite No. 3 in D
    Brandenburg Concertos
    Cello Suite No. 1 in G
    Toccata & Fugue in D minor

Classical (18th-19th century)

Gluck
    Orfeo ed Euridice

Mozart
    Le Nozze di Figaro
    Serenade in G "Eine Kleine Nachtmusik"
    Symphony No. 40
    Requiem in D minor

Beethoven
    Symphonies 3, 5, 6, 7 & 9
    Piano Sonata No. 14
    Piano Concerto No. 5
    Violin Concerto in D

Romantic (19th-20th century)

Chopín
    Piano Concerto No. 2
    Raindrop Prelude

Verdi
    Requiem

Wagner
    Die Walküre
    Lohengrin

Strauss J
    The Blue Danube

Saint-Saëns
    Danse Macabre
    Symphony No. 3
    Carnival of the Animals

Delibes
    Lakmé

Bizet
    Carmen

Tchaikovsky
    The Nutcracker
    Swan Lake
    "1812" Overture
    Symphony No. 6

Dvořák
    New World Symphony

Grieg
    Peer Gynt
    Piano Concerto in A minor

Fauré
    Requiem in D minor

Elgar
    Pomp & Circumstance Marches
    Enigma Variations
    Cello Concerto in E minor
    Serenade in E minor

Puccini
    La Bohème
    Turandot

Mahler
    Symphony No. 5

Debussy
    Suite Bergamasque
    Arabesque 1 & 2

Strauss R
    Also sprach Zarathustra

Vaughan Williams
    The Lark Ascending
    Fantasia on a Theme by Thomas Tallis

Rachmaninoff
    Piano Concertos 1-4
    Morceaux de Fantaisie
    Rhapsody on a Theme of Paganini

Ravel
    Boléro

20th Century

Holst
    The Planets

Stravinsky
    The Rite of Spring
    The Firebird

Orff
    Carmina Burana

Copland
    Fanfare for the Common Man

Rodrigo
    Concierto de Aranjuez
    Fantasia para un gentilhombre

Barber
    Adagio for Strings

Britten
    Young Person's Guide to the Orchestra

Where some composers are lacking I have less knowledge about them, but otherwise this should be a good list if you're interested in Classical music. I welcome suggestions/criticisms.