THe FF8 Configurator v2 (available at
FFSF) can play the game music (on the "Sound & Music" tab) -- but you don't get to see the song titles like you do in FF8 MIDI, just the file names. So, there's a memory-leak-less alternative.
Also, there's a Winamp plug-in to let you play FF8's .sgt files in Winamp.
I haven't tried FF8 MIDI in a while, but back when I used it on a Win98 machine with 128 MB RAM, after a while of use, the program would start getting all slow and crash, and I would just restart the machine. Try it out and see how it works for you...