Shaking the Wii remote is integral to Wario Land: Shake It. Nintendo emphasized this since “shake” is in the title. What does shaking do? Lots of things, but there are basic platforming controls too. Reminiscent of Wario Land: Super Mario Land 3 you move with the D-pad, jump with a button, and shoulder tackle with another. Jiggling the controller makes Wario do a ground punch which makes blocks sitting on the edge of platforms tip over, opens doors, and stuns enemies. When in doubt or frustrated because you can't figure out what to do next, shake.
The most iconic image of Wario Land: Shake It is seeing Wario rapidly shake a money bag. You get to do this with the Wii remote and use the same motion to steal items from creatures. Wario Land: Shake It also uses motion control, specifically rotating the controller, to aim where Wario chucks a stunned creature and to shift his weight while riding a mine cart. None of these innovations seem like they couldn’t be done with simple button presses, but shaking items out of enemies sounds like fun.
Images courtesy of Nintendo.