I was looking for this thread I have so many favorites, I grew up listening to classical music. In no particular order:
My first two are by Chopin. The Winter Wind Etude (Op. 5 #11) and the Ocean Etude (Op. 25 #12). That last one I've played, albeit not as well as Lang-Lang. The other two are goals, but my arm hasn't quite been the same since mastering the Ocean.
Then there's the classic Carnival of the Animals by Saint-Saëns. My favorite of the bunch is VII: Aquarium.
Last but not least for now, Dvorak's New World Symphony. The 4th movement is most famous, but the whole thing is absolutely worth a listen.
A little bit off the beaten path, but Max Bruch's Scottish Fantasy suite is one of the most evocative and story-like pieces of classical music I've come across:
I am partial to Rachel Barton Pine's version, but this one is very nice as well!