You can play Tatsunoko, Brawl, Mario Kart, and a few other games, using your Wii, but it has to be through USBLoaderGX (or WiiFlow) using a hacked ISO.
The Wiimmfi program will do this.
Here's instructions on how to do it with Brawl (Project M version). There is, I believe, a similar method for Judgment, but it has to be found:
**clicky**EDIT: it may be possible to do this with an official disc using Gecko or Riivolution but I don't know enough about it.