I got out of my car this morning with the intent of listening to my iPod Nano (4GB), and the LCD screen just flashed the dead battery icon. I had just charged it full since it was dead last time I went to use it. I figured it was just because I had left it plugged into my iTrip Nano. So I was about to go buy a new iPod Nano (1GB this time... little short on cash right now) when I realized that my alarm on my iPod was waking it up and playing it until it died.
The moral of the story: If your iPod dies a few times in one week, check the alarm clock.