Its very unlikely that stock wii's will ever play DVDs.
Nintendo has a longstanding history of designing its consoles with one purpose in mind - to play games. It is one of their strongest points, and its why the do it better than everyone else
The Xbox/360/PS3 consoles are all designed with multi-media in mind - not just gaming. In addition to focussing the console on gaming (for the most part..I know that it can play videos via the photo channel but thats not really a feature due to how you do it), DVD playback hugely increases the unit cost of each console due to the licencing requirements. Nintendo have been quoted as stating that the hardware is technically capable, but that they have not included the required software in order to keep the costs down.
The gamecube was also technically capable of playing DVDs - but it lacked the software (you could insert full sized DVDs to a GCN by removing/replacing the top shell).
Whats likely is that a 3rd party will be authorised to produce a multimedia version of the Wii - similar to the Panasonic Q version of the GCN which will be DVD capable. It is highly unlikely that it will make it out of Japan though, and most probably won't be branded as Wii or as a Nintendo product...but thats just an educated guess, I'm sure its possible for Nintendo to release a download to enable it (probably at a cost to cover the licence), and theres no reason why some homebrew code couldnt be thrown together to enable DVD playback. That would [currently] require a mod-chip though.