A list like this could go on and on - and is very likely to cause some debate - but these pieces all played big parts in my development as a musician. And I, too, love "The Planets".
The Firebird
- Igor STRAVINSKY
The complete ballet is the way to go. Much more rewarding than the concert suites.
Scythian Suite
The Love for Three Oranges (Ballet suite)
- Sergei PROKOFIEV
If you are especially partial to the bigger movements (Mars, for instance), prepare for a big treat. The Scythian Suite's finale (an huge musical depiction of sunrise) still stuns audiences.
Pines of Rome
Fountains of Rome
Roman Carnival
- Ottorino RESPIGHI
I second the recommendation previously mentioned. Don't miss these.
Pacific 231
Rugby
- Arthur HONEGGER
Two musical expressions. The first work gets its name from the steam train. The sounds of the steam venting, accereration, coasting, and slow, gradual stop are all extremely vivid. Rugby is a more abstract, but no less exciting, musical expression of - surprise - a rugby match.
Prélude à l'Après-midi d'une faune (Prelude to 'The Afternoon of a Faun')
Nocturnes
- Claude DEBUSSY
If you like the quieter, ethereal momements in The Planets, you'll enjoy these pieces. The third movement of Nocturnes, "Sirens", even has an otherworldly wordless female chorus, like Neptune.
La Valse
Daphnis et Chloé (either the second ballet suite or complete)
- Maurice RAVEL
Ravel, generally speaking, writes with a more delicate touch, but all these works are not only masterpieces in the orchestral repertoire, but should appeal to anyone fond of The Planets, too.
Appalacian Spring
- Aaron COPLAND
Down-to-earth and definitively American, but I think it's fair to say if Holst were American, he just might have produced a work like this ballet score. I prefer the orchestral version for its much more colorful sound (or "tone palette"). Purists like the original version for small ensemble. My advice: Go for the full orchestra and if you fall in love with the piece you can always pick up the original.
Estancia (Ballet suite)
- Alberto GINASTERA
Add "Latin" before "America" in the paragraph above and you'll be close to the mark. The final "Malambo," a dance of endurance, is a guaranteed crowd pleaser (see how the reserved Swiss audience reacted when the Simón Bolívar Youth Orchestra played it in Luzerne: http://www.youtube.com/watch?v=qw1Z2ebqe_s)
Short Ride in a Fast Machine (from "Two Fanfares")
- John ADAMS
The most frequently performed work by a living American composer for good reason. The music is meant to invoke the feeling one gets riding a rollercoaster.
And because it's getting late, I'll offer these without comment:
Pictures at an Exhibition (orchestrated by Maurice Ravel)
- Modest MUSSORGSKY
Four Sea Interludes from "Peter Grimes"
- Benjamin BRITTEN
Symphony No 2 ("Mysterious Mountain")
- Alan HOVHANESS
La croqueuse de diamants (The Gold Digger [often mis-translated as The Diamond Cruncher])
- Jean-Michel DAMASE
Featured in the film "Black Tights"
The Red Shoes
- Brian EASDALE
From the film of the same name