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Nintendo shipped 20.05 million units as of dec 31st 2007.
Nintendo themselves say that it takes 3 weeks to get from them to retail floor in US and EU.
Given a monthly production of 1.8 million units this means that at any one time there are roughly 1.35 million Wiis in transit around the world.
This gives us at least 18.7 million units on retail floor as of dec 31st. It takes less time to ship to Japan so the number will be a bit higher.

VGChartz has the number of Wii sold at 19.07 million. Seems pretty accurate to me.