The first mod I ever heard was my own, dunlending.it... and it sucked - bad. I probably caught on pretty quickly how to use ModPlug Tracker (just took 2 minutes actually for me to figure out the basics, I think), but it's obvious that my early 2004-2005 modules were all, well, crap.
The first mod that I didn't make myself that I heard were probably a bunch of module soundtracks from old school classics on the Amiga like Blues Brothers and a few others (I forget).
Basicly, my personal tracking biography is pretty dull...
EDIT: Remembered the names of the games.
Oh, and how did I find out about trackers to begin with? It's quite a dull story, too. I wanted to make my own music for my games and found my old tools to be rather inadequate (MS-Sound Recorder, my Yamaha PSR-280 and a microphone on the speakers. I also did some stuff by fiddling about with my voice, which can be heard in my oldest games).
I asked my friends about if they knew any free program that could make music and my friend Tony (Chunitana) told me that ModPlug Tracker was good. I asked another friend later over MSN who also appeared to be tracking for some samples and he gave me a few .XI instruments, I loaded them up and got going. The result after half an hour of tracking: dunlending.it - A fairly bad, partially out-of-beat drum and bass tune (the bass melody was pretty OK, though, the drums were incorrectly timed in two patterns by 1/16 or 1 row).