The Nintendo support site recommends using channels 1 or 11, which are too crowded in my area. I can't find any documentation on which channels the Wii actually supports.
It would depend on your country more then likely, for example the US has 1-11. While the rest of the world usually has 13, and Japan having 14.
If you are in the US, The Wii would support 1 to 11. This is controlled by your router settings. What channel your router is set to broadcast at is what channel the Wii is going to connect at and send data through.
Since this is controlled by the FCC on what frequency the wireless devices can use. If it is being sold in the US it is required only to support channels 1-11 on the 2.4 GHz level.
More information can be found looking at this ISM band article. This is the reason why cordless phones/bluetooth/wireless routers all operate at the usual ISM band because they are unlicensed and free to be used by anyone, meaning you can't complain to the FCC if you get signal interference using these frequencies.
My recommendation if you have an Android phone would be to install this application Wifi Analyzer, this will allow you to scan your area and pick the best channel with the least amount of interference. Note that for example channel 11 overlaps channel 9 and 10. This will allow you to pick the best for your area. As you would get a graph looking something like this.
Sadly if looks like Apple has removed all apps that would accomplish this same thing on the iPhone from this article. There are probably jailbroken apps that can accomplish this, but I am unfamiliar with what is available..