I really can't remember... I don't even know which the first classical piece I've ever listened to was! Then, I was in all likelihood inside my mum's belly!

My mother and my grandparents love classical music. Since I remember myself, I have been listening to classical music.
When I was a toddler, my mum had some
Mozart CDs. I used to listen to them.
Symphonies (especially
the 40th, which I still love listening to!),
Piano Concertos (I still remember listening to
the 9th),
Eine Kleine Nachtmusik and, of course, his
Piano Sonatas.
At my grandparents house, I used to listen to
Rossini's "Il Barbiero di Siviglia" and
Beethoven's 3rd, 5th, 7th and 9th Symphony. All these were and still are my grandfather's favourite and certainly remind me of my childhood! As for my grandmother, she likes
Beethoven's Piano Sonatas and
Schubert's Serenade. I must have listened to all them pieces for about a million times!
Finally, both my mum and her parents reaaaaaally adore
Chopin. I don't think I have to exlain anything here!
Waltzes, Nocturnes, Polonaises, Impromptus were "favourites" at my home!

Anyway, interesting question by nanabush!
I can't hold back my tears when listening to all these masterpieces!
