If you've been on the moon for the last couple of years you may never have played on a Wii. Its main selling point is its (for the time) unique control method. Imagine playing a video tennis game where instead of pushing on a couple of buttons, you actually have to swing your arm in a serving fashion in order to serve. Add to that the optional Wii balance board and a plethora of other add-ons, then you have a virtually complete home entertainment and fitness system.
I say virtually complete, because the only criticism I have of the Wii is that you cannot play DVDs on it.
You do have access to literally thousands of games though. Indeed, all the old Nintendo games can even be played on it. You turn the remote on its side and it behaves like a good old fashioned gamepad. Just about the entire back catalogue is available to purchase from the Wii store. You access it from the Wii itself (& it has a fully functional browser so you can even use the Wii to surf the net). Not every game in the store is a blockbuster (popup pirates sucks, for instance) but there are some good finds in there if you have a browse.
The Wii console is the most family friendly games system out there. You will need to invest in some extras, such as additional wii remotes, and dancemats, to get its full potential, as it really excels at multiplayer games. However, even the basic system offers hours of family fun.
Just get one.