You get one controller and one nunchuck with the console. If you buy the Wii Play for the extra controller, it doesn not come with a nunchuck (Wii Play is a $50 game that comes with a controller. A lot of people buy it because a controller alone costs $40, so you are basically getting the game for $10).
We are a family of 4 (kids ages 7 and 9) and we started out with 2 controllers last Christmas and two nunchucks. Within about 6 months, we bought 2 more controllers (but did not buy 2 more nunchucks), that way we could all four play, or when the kids have friends over more than two can play. We are very glad we bought the two extra controllers.
We do have one wheel to use for MarioKart, but it is just as easy to not use the wheel.
Other than that, we don't have any of the extra "stuff" for the Wii, and I really don't think we need it (unless, you are talking about the board, which you may have to have to play certain games.)
We love our Wii!!