The Atari ST was a wonderful computer, but technically speaking, it was inferior to the Amiga on almost every aspects. One of those was the sound circuit: the YM-2149 soundchip found in the Atari was capable of generating three voices of square waveforms (meaning flat and synthetic sound) whereas the Amiga's chip (codenamed Paula) could render four voices of wonderful form-free sound.
But there were many composers on the Atari nonetheless and some were extremely talented (a few of them being Mad Max, Scavenger and Count Zero). Having to work with such a poor instrument as the YM, they developed a great cleverness to produce great tunes with many original coding tricks and composing skills. Some of the tunes they produced are in my opinion some of the best computer music ever made, but hey, that's an Atari lover speaking, right? ;-)
A note on listening to Atari ST music on recent computers: there is a french demomaker called Leonard from the group Oxygene which made a YM-2149 emulator called STsound which allows you to play Atari (as well as Amstrad CPC and Sinclair Spectrum) music files stored in small files (a couple of kilobytes per song) and which sounds quite good. Unfortunatelly, this person never released the source code to his player and thus, people using exotic operating systems like linux or macOS cannot use it. I've tried contacting him to make an XMMS plugin for linux based on STsound, but I never got a response. Oh well.
update 2005-04-08: Shame on me! There was that great project called sc68 that released a free and open-source player for Atari ST tunes, along with an extensive archive of Atari ST tracks! Oh Joy, Oh bliss!
I've quickly made two Debian packages with the sc68 player and the XMMS plugin for Debian users to enjoy this great program.
And guess what: now that I have found an open-source project for playing ST tunes, I just found out that Leonard made STsound open-source two month ago :-/ Well too late for that, I'll stick to sc68.
What you'll find here is 128 kbps mono MP3s of a couple of songs from the Atari that I like. I recorded them directly from my old ST and encoded them with gogo.
update 2007-07-08: Here are a few new (!) ST tunes, that I discovered on Kohina and re-recorded from my ST: