What is the biggest SD memory card a Nintendo Wii can support?

With Wii Menu 4.0 and above you can use up to 32gb SDHC cards. Full details can be found on Nintendo's customer support site.

You can use SD, SDHC and miniSD or microSD with adapters.

The other thing to bear in mind is that some (older) games won't recognise larger cards so you may end up having to buy several cards anyway.

We have a 8GB card that the kids store Wii channels on that works just fine, but Guitar Hero won't recognise it so we have to use a 2GB to store the GH downloadable content (extra songs etc.)

I think the important thing to note here is that the wii seems to prefer Fat and Fat32. Fat32 maxes out at 32gb, so anything larger than that is going to probably get stuck in NTFS or exFat and the Wii isn't going to know what to do with that. If you had something larger than 32gb, you could partition it, but most likely you'll only be able to read the first partition, which can only be a maximum of 32gb. So.. 32gb, that is basically the max.