The mod is still early in its stages of development, but it has been demonstrated to work between a Wii and a Wii U both playing New Super Mario Bros. Wii (and splitscreen Mario Kart Wii as a proof of concept). The mod won't allow single player games to become multiplayer or allow for more players than normal, but it will let you play with other people across the world online, even for offline multiplayer games. It even works if a player enters the Wii's Home screen.
As of now, there are a few limitations: it's fairly easy for the players to desynchronize (shaking the remote will do it, for instance) and loading times are extremely long. Also, half the screen is covered by a console, but that is only for development purposes. It's likely that certain games will also require game-specific fixes in order for them to be fully functional with this mod. Using the same mod, it will also be possible to act as a spectator to another player's game session and playing GameCube games and Virtual Console games online may also be possible.
|It's pointless, but as a proof of concept, you can also play splitscreen MKWii multiplayer online.|
Update: Official demonstration here.