BobM (and Marie-Claire), thanks for this.
I just assumed recording equipment was currently beyond my means, but on Friday, after reading your post, I downloaded Audacity, stopped by a Radio Shack, and made my first recordings. Total cost: $21.79.
Once I figure out how to make a decent recording, I'll post something. My first attempts weren't terrible, but I think I had the microphone too close to the soundhole - tubby bass, shrill trebles, and string squeaks that sometimes overpowered the music, plus a few stray popping sounds that I'm pretty sure my guitar didn't actually make. Still, it's interesting to be able to hear my playing without needing to think about what my fingers should do next. I can put a lot more thought into what I might want to change next time I play the pieces I've recorded.