Thanks to all of you for your replies.
I'm hoping to get a chance to look it over this weekend. I'm hoping it's something as simple as a ground, bad battery cables, or the alternator.
Those were my first thoughts, particularly the alternator, but I was afraid of something more like HotRod Rocker, or Bruck K is talking about.
I started it up late last night, after I got home, and it didn't seem to be having any of the issues I experienced the night before.
Oh well, at least it gave me an excuse to drive the truck downtown.
I'll let you know what I find out.