You can, and it's actually called "homebrew," which is one of those words that always sounds like a neologism (a newly coined word) but in fact originated in the mid-nineteenth-century, meaning "an alcoholic beverage made at home." Go beer, then, and what's more, go who'd-a-thunk-it hacks that let you for-real load Linux and "embrace your inner penguin" on an unassuming white box half the size of a toaster.
Complete instructions and files are here.
You'll need a GameCube SD card adapter, a 1GB (or higher) SD card, a copy of Zelda (for the Wii), and of course, a Nintendo Wii itself. Next, you'll need to make sure your version of Zelda is one of the anointed -- apparently not all copies of Zelda are created equal. Finally, you'll have to do a bunch of extracting, copying, renaming, deleting, saving, etc., load the game, load a hacked save file and actually talk to a guy in-game to trigger the loader, which drops you out to a black and white screen, at which point you get to have fun figuring out how to load Linux itself. I don't pretend to understand it, nor do I have any intentions of trying it, but if you just want the thrill of getting away with something Nintendo doesn't want you to, by all means go for it.
See earlier story here
Source: PCWorld