I believe the Wii manual states a fresh set of alkaline AAs last around 30 hours. The number is a rough estimate since the amount of time the batteries last fluctuates depending on how you use the remote. I asked a Nintendo representative how the 1:1 the newly announced Wii MotionPlus accessory will affect the battery life and was informed you only get 9 hours of battery life when you use it. He stressed this accessory is still a prototype and they are working on improving the battery life when the completed hardware comes out in the spring.
Images courtesy of Nintendo.