Nintendo America president Reggie Fils-Aime told the press that Nintendo DS will soon be able to download demos and even buy whole games from the Wii console:
The games and demos will presumably be downloaded through the online Wii Shop Channel and then transferred to the portable via the wireless capabilities of both systems.
Though word of downloadable demos comes as little surprise--DS Download Stations located at retailers already allow such functionality and Nintendo previously announced it would come to the Wii someday--the inclusion of full games is a bit more surprising.
It is unknown if that full games bit refers to digitally distributed versions of existing games, compatibility with downloaded Wii Virtual Console titles, or WiiWare software specifically designed for the portable.
At present, the Nintendo DS can only hold one demo at a time in its internal memory. Once downloaded, users cannot power off the system or run any other software without losing the demo.
UPDATE: Nintendo announced this information wasn't correct. DS owners will not be able to purchase full games, only demos will be available.