Just 2 days ago it was reported that full DS games would be made downloadable thanks to the wifi comparabilities of the Wii. Well it turns out that was a mistake made by The New York Times and, like the Japanese version of the same channel, only DS demos will be available to download.
From Nintendo: "An article about the Nintendo DS video game system in the Dec. 31 Business Day section of the New York Times incorrectly referred to future capabilities of the device. The statement that complete Nintendo DS games will eventually be able to be downloaded into the device via a wireless connection with the company's Wii game console is incorrect.
Users can download games to play on Wii, and, in the future, the Nintendo DS will be able to receive demo versions of some DS games from Wii, but not the entire game. The demo will be erased once the Nintendo DS is turned off."
Source: Nintencast