Someone mentioned Timidity earlier... if you're using Linux and ALSA, it is possible to use Timidity with DOSBox (assuming you're using fairly recent versions of both).
Start Timidity in ALSA server mode, and make sure it's set to use ALSA (not OSS) for sound output, e.g.:
timidity -Os1S -s 48000 -a -iA
Yes, the syntax is quite obscure: "-Os1S" means "ALSA, 16-bit, stereo", 48000 is the sample rate (might want to use 44100 depending on your sound card, or 22050 on a slower computer), "-a" means use the anti-aliasing filter (might want to disable this on a slower computer) and "-iA" means run as an ALSA server (receives MIDI data from other programs rather than a file).
Add the following lines to the [midi] section of dosbox.conf:
device=alsa
config=128:0
The number after "config" is the ALSA MIDI port used; you can set it to anything you want but 128:0 is where Timidity listens by default.
Make sure SDL is set to use ALSA for sound output; type
export SDL_AUDIODRIVER=alsa
Then start DOSBox, set your game to use General MIDI, and if you've set up Timidity with the appropriate patches, the music should sound exactly like it would on a GUS.
Timidity can also use Soundfont 2 patches; if you use AWEROMGM (available here or here), you can make the music sound almost (the patch set isn't perfect) exactly like it would on a Sound Blaster AWE32.
Since Timidity is a software synthesizer it will take some CPU time away from DOSBox; with more demanding games you may have to trade sound quality for speed. But it has the advantage of working even with simple built-in motherboard sound chips that don't have their own wavetable synthesizer.