As of today, it is not possible. Not even for the DSi. Sure you can use DS Download play using a certain Wii channel to play trials of new games, but you cannot play Wii games on any current version of the DS. There are some titles that are in both the Wii's and DS' library, but that is completely irrevelant.
You cannot play Wii games on any Nintendo DS system.
Yes, the NDS lite can play all DS games
No. There is no way to download or play DSiWare games on Nintendo DS or DS Lite systems.
It can play GameBoy games and DS games.
Yes, the original Nintendo DS as well as the Nintendo DS lite can play NDSi games.
You cannot play Wii games on any Nintendo DS system.
Yes, the NDS lite can play all DS games
Yes you can play Nintendo DS games on a Nintendo ds lite.
you can't play ds games on your wii
No. But, you will be able to play ds lite games ont the 3DS.
No. There is no way to download or play DSiWare games on Nintendo DS or DS Lite systems.
It can play GameBoy games and DS games.
Yes, DS games are region free.
There is no such thing as a DS Lite game they are all just DS games. So, yes, you can play them on the old DS.
No, the Wii U cannot play Nintendo DS games
yes you can.
no you can only use Nintendo games on Nintendo ds/Nintendo ds lite.