My 40GB, firmware v2.1, bought Jan 2004, Apple iPod has peculiar charging habits.
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The alledged problem with the iPod is well covered over the 'net (1 2 3 4 and 5 just to get started}}. I've been using mine pretty extensively over the last few weeks, and have noticed weirdness with charging.
To replicate the 'problem':
1) Use your iPod
2) Make a note of the battery symbol in the top right of the screen's level.
3) Charge your iPod (for lots of hours, like perhaps overnight)
4) The full screen battery charging indicator will say "charged" and will show a full battery.
5) Unplug your iPod and press "menu" to turn it on (without spinning up the disk)
6) See the battery icon shows some small amount of charge? (Mine's shown half full, "one blob" and even one pixel width above zero)
7) Re-plug in your iPod
8) It charges all over again, and for some considerable time (you might expect a few minutes as it sorts itself out, but not a few hours)
I've used my iPod for many hours after (6) and (8), so I'm not sure if it really does charge, if it fakes it, or what. My iPod's new, so I guess I'm less likely to run into problems than a slightly older one.
So, methinks it doesn't really know how charged the battery is, or how much more to charge it, or something. I'd imagine a firmware fix would solve the problem though. EIther way, right now it's screwed. I guess I'll find out what the deal is in a year or two's time when the battery fails ;-)