Miis are Digital Avatars used in Nintendo software. Debuting with the Wii, Miis are meant to be multipurpose characters that can be used in a variety of ways. Mii support has since been included with the Wii U and Nintendo 3DS as well.
Note: Due to the nature of Miis and how they're used, tropes may not apply to every place they appear.
Adaptational Badass: In Super Smash Bros. For Nintendo 3DS / Wii U, Miis come in three different varieties (Brawler, Swordfighter, Gunner) and can stand up to even the likes of Bowser, Ganondorf, and other Nintendo heavyhitters. Sakurai even states in their introduction video that they were "toughened up" to be ready for Smash.
Author Avatar: Miis of Nintendo employees are commonly seen during game trailers that use Miis.
The Backwards R: The Wii allows Greek letters when naming a Mii. Many players use the Greek letters for this trope. For example, a Mii going online for Mario Kart Wii might be named "ρlαγεr" rather than "player". The Nintendo 3DS and the Wii U allow both Greek and Cyrillic letters, though fewer players seem to be using them.
The Cameo: In some games, Miis only serve as background characters.
The first time a Mii could talk was in Mario Kart Wii, what voice depends on the color of the Mii's shirt. They could talk again in Mario Kart 7, except they'll always have the same voice, regardless of the shirt.
Miiverse posts can also count as talking, seeing how they move their mouths on Wara Wara Plaza.
Cartoon Conductor: When the curtains are closed there's a chance that the Mii will twirl a baton.
Cartoon Juggling: When the curtains are closed, there's a chance that the Mii may juggle 3 colored balls. At the end, it throws the red ball in the air, spins, and then catch it in his hand.
There's also a variation in which he fails doing this.
Catching Some Z's: When the curtains are closed, there's a chance the Mii will do this, and then wake up and make a bashful expression.
Pull a Rabbit out of My Hat: When the curtains are closed there's a chance that the Mii will pull a dove or a bouquet of flowers out of a hat.
Rock-Paper-Scissors: There's a chance that the Mii will play this with the player when the curtains are closed, albeit using hold up signs with the symbols on them, because of the Powerpuff Girl Hands trope above.
Say It with Hearts: When the curtains are closed there's a chance that the Mii will sing, complete with musical notes coming out.