Nintendo has set an expiration date for all Wii and DS online software functionality: May 20th. As of that date, any online play for titles on those consoles will be rendered kaput. This includes Mario Kart Wii, Pokemon Black & White 2, and numerous others.
Note shutting down servers for online play does not render digital software obsolete. In fact, despite the server cut, both the Wii and DSi eShops will continue to process transactions. Undoubtedly, the backwards compatibility of Wii U and 3DS save these marketplaces from immediate closure.
The full list of games is available via Nintendo’s Wii & DS Wi-Fi connection service page. Nintendo does not state a specific time for the cut off.