“Are there any limits to how many channels you can have on the Wii?”
The Wii can hold up to 48 channels and that includes the channels that already come with the system like the Mii, Weather, and Photo channels.
If you find yourself needing more room for channels you can delete the ones you don’t use. You can always download the channels you deleted again without paying again.
There are some channels that cannot be deleted like the “Disc Channel”.