Impressed by Jeremy Shatan’s answer, to have included the Fourth Symphony! So Mahler, so anxious, so my favourite, and not often heard. The Cello Concerto #1 speaks well to Jeremy’s taste as well, but that piece is better known.
So, skipping those two:
- Ninth Symphony. Jolly, quirky, Haydn on steroids, alternating with genuine lamentation in the 2nd and 4th movements. (Bernstein thought the 4th movement was a parody of Beethoven’s 9th; I’m not seeng it.)
- 24 Preludes and Fugues. It may not be more formally perfect than Bach’s, but it has a much more prodigious emotional range, from the sunshine arpeggios of #7 to the tears of #24 to the insanity of #15.
- String Quartet #8. A lot of extramusical lore has built up around this “suicide note”, and not unreasonably, with Shostakovich quoting himself repeatedly; but the music supports it. Harrowing.
- Seventh Symphony. Not so much for the famous first movement, as for the solemn mass of the third, grieving and angry and soulful.
- The Anti-Formalist Rayok is not a favourite piece, not even a particularly great piece, but its passive-agressive sniping at Stalin and Zhdanov is certainly instructive about where Shostakovich was at in 1948. Bonus for the YouTube performance featuring Stalin sung by a guy with a Stalin moustache and a Stalin pipe.