They say use only Alkaline batteries because of the voltage output (1.5V) whereas rechargables only put out 1.2V which could result in irregular or incorrect Wiimote behavior. It's bollocks though, because if you're only supposed to use non-rechargables, you'll be buying batteries every freaking week!
They say you'll get 20 hours of use out of a pair of AAs, but when you think about it really is not that much time, given you play for let's just say 3-4 hours a day, you'll have used up your batteries in about a week.
I can't help but wonder why Nintendo didn't consider the battery dilemma we'd all face... Why couldn't they do something like what they did with the DS, where it has it's own proprietry battery design built for the intents and purposes of the device, not to mention being RECHARGABLE. The DS also had docking stations available. I sure hope the Wii follows suite.