Yes! There has been LOTS of great classical music composed in the 20th Century. Some of my favorites CD's containing modern classical music...
HOVHANESS: Celestial Gate & Other Orchestral Works
Moods invoked by this music: celestial, noble, majestic, melancholy, mysterious.
GORECKI: Symphony #3 "Sorrowful Songs"
Moods: sacred, mourning, anguish, rapturous.
VASKS: Message
Moods: ethereal, other-wordly, yearning, soaring.
SHOSTAKOVICH: Symphony #8
Moods: dark, brooding, patriotic , frenetic, apocalyptic.
(BTW: The CD's listed here contain some of the absolute best performances/recordings of these symphonies. These are definitely CD's to play if you want to test and/or show off the high fidelity of your stereo system.)