I've been waiting for this one! I wonder if we are also doing any other periods of Western Art Music, like Renaissance or Baroque, for example?
Here is my favourite piece from Luigi Boccherini (1743-1805),
String Quintet No. 5 in E Major, Op. 11: III. Minuet. It is probably also his most famous piece of music.
Everyone knows the first movement of Beethoven's "Moonlight Sonata", but my favourite movement is the third:
A beautiful piece of music from Mozart, highlighting the harmonic achievements of the
Common Practice Period.
Requiem in D minor, K. 626: Sequence VI. Lacrimosa Dies Illa. This movement, along with the subsequent movements in the Requiem, were left unfinished by Mozart due to his death - they were completed by Franz Xaver Süssmayr, a student of Antonio Salieri (and that is how he was associated with Mozart)
Johann Ludwig Krebs (1713-1780),
Fugue in Bb Major
A beautiful harpsichord piece by Armand-Louis Couperin
La Chéron
That's all I can think of for now, enjoy