On the evening of November 18th, 2006, Nintendo was preparing for the midnight launch of the Wii console in Times Square New York. The video below is an overview of the launch. If you skip to 6:20 in the video, you will see Reggie officially announce the opening of the Wii Shop Channel, which launched with 12 games. Check out the video below.
The Wii Shop Channel will close for new purchases on Thursday, January 31, 2019 at 2:59 PM Japan Time (which I believe will be Wednesday, January 30th, 2019 at 10:59 PM Pacific Time, but I could be off a few hours)
It's been an amazing 12 years of service!
If you have a Japanese Wii with Yen/Points left on the Wii Shop Channel, you can exchange that money for a Nintendo eShop card for the same amount for the 3DS/Wii U. Based on the information, a special "Wii Shop Channel Password" will display on the shop starting on February 12th, 2019 which will help with the conversion of your points. All the details about this is right here:
It is unknown if this same transfer process will happen in other regions.