This has been gone over before in other forum threads, but let's give it another shot...
The Wii's specs are not adequate to the job of running Hedgewars. Not enough vRAM or RAM for a pixel based game.
The Wii has 88MiB of RAM. Total. 24MiB of that appears to be for graphics, 64MiB for system. Of course some of that memory would have to go to running the system.
Using latest dev version you could possibly play small sized maps on a Wii, but I doubt it, once you consider supporting libs and the OS.
But you'd still have to figure out how to compile for the Wii - that means functioning SDL and GLES2 for the Wii.
I'm unaware of any project to do that.
So. It would be a very difficult task and be unlikely to yield useful results.

Netbooks should be able to run Hedgewars. Try disabling compositing if you are using Windows (turn off Aero - in fact, set settings to "optimise for speed").

Pastebin game0.log if you'd like us to check your graphics driver.

You can also try Reduce Quality in settings.

So...Hedgewars runs on Android but not on Wii?

Yes.

I agree a Wii version would be pretty cool, but it's obviously not going to happen.

Android is an OS, Wii is OS + hardware.

But. Here's the issue. Wii has, as mentioned, 24MiB for graphics, 64MiB main memory, and 3MiB(!!!) for texture memory.
By comparison to that 3MiB, even a low-end graphics card from a years back for the desktop would have at least 64MiB.

For a sprite based game, texture memory matters a *lot*.
Most wii games are not texture heavy. But, consider the land in hedgewars. If the land fills about a third of a playing area,
even w/ blurry land enabled (upscaled textures that look kinda ugly) that's 2048*1024*4 / 3 - or 2.67MiB of texture memory. And that's not including alll the other sprites (weapons, animations, hedgehogs, hats (hm, I guess these could be skipped. would look kind of ugly), background textures (could be skipped) flakes (could be skipped) )... I'd say the lowest we could practically go at max reduce quality is probably more like 4-8MiB.

Texture compression would help, assuming the Wii had it, and it was in a non-proprietary format, and someone was willing to write support for it, but we are still basically out of space on texture memory.

And that's not getting into that 64MiB to run both the OS and the game and the libs. And the game needs quite a bit of memory for the in-memory representation of the playing area. 4096x2048x2 - 16MiB just for Land[]. Add LandPixels, even at ReduceQuality (2048*1024*4) and you are up to 24MiB - and still need room for all the other data structures. From our experiences on the first gen iPhone (yes, Hedgewars ran on the iPhone from 2007) I'd say Hedgewars needed about 50-60MiB of RAM to run, not including textures. And that was with the smaller playing area which only took 6MiB of RAM instead of 24MiB - the rest was the game and supporting libs.

Even the 1st gen iPhone has 128MiB of RAM - it shared it w/ the gfx card for texture memory, but 64 + 3 is waaaaaaay smaller than 128.

So. Let's compare the Wii to, say, the Samsung Galaxy Note phone - no. not the new one, the old one...
memory. Wii: (64+24)MiB Samsung Galaxy Note: 1024MiB
cpu. Wii: 729MHz PPC (90nm) Samsung Galaxy Note: dual core 1500MHz ARM (48nm)
vram. Wii: 3MiB Samsung Galaxy Note: whatever the OS and game isn't using of that 1024MiB (could be as much as, oh, 700MiB or more)

In short. There's a huge difference between a console and a smartphone or computer