Thanks to Dan <firstname.lastname@example.org> for this original information.
Note: To the best of Dan's knowledge, the programs mentioned here can be downloaded via ftp from ftp://atari.archive.umich.edu/ and its mirrors. Using the same address in any browser should also allow you access.
Atari ST: There is a port of ProTracker from the Amiga. This will allow you to create 4-track MODs.
Atari STE/TT/Mega STE: To create mods on these machines, you basically have a choice of two programs - ProtrackerSTE or Octalyser.
ProtrackerSTE is an upgraded port of ProTracker from the Amiga. It handles only 4 tracks, but has the full PT command set and gives good quality playback. (Note there are also a bundle of PT clones for these machines, such as Esion)
Atari Falcon030: For creating mods on this machine, there are basically three main choices:
Octalyser (mentioned above) has drivers for the enhanced sound system, thus giving good quality playback, but only 4, 6 and 8 track mod formats, not S3M or MTM.The following updated 1999 information was supplied by the wonderful efforts of frustrated Atari owner James Smith email@example.com who contacted me on absm complaining about the lack of Atari playable MODs. He found this tracker, and few other bits and pieces (see players)....
DBE Tracker It is worth noting that this is the newest multichannel tracker for the ST. Unlike Mega and Graumf Trackers, DBE will run on ALL Atari machines and will attempt to play up to 32 channels on any of them. Obviously there is a serious loss of quality on lower spec machines... A demo of the programme is available from many Atari sources and it can be registered with the author (Denis Huget) for about 6 UK pounds. Updates are provided on a regular basis to registered users.
I checked that the original links still worked but I couldn't connect to ftp://atari.archive.umich.edu/atari/Music so I wasn't able to verify any Atari information. Any further Atari help would be most appreciated...but I nosed around a bit more so try these sites..
http://www.incontrolinternet.co.uk/atariwebring/ - Atari Music Webring of 160+ sites! Proving that there is still life in the ol' dears yet!