No. All games are region locked much like DVDs are so a console bought in the UK are not going to be able to play US or Canadian games.
The way around that is to mod your Wii, which if done incorrectly can turn it into an expensive paperweight. Some places you may be able to chip it so that it will play all region games.
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Currently the largest library of games for a Nintendo console is the Nintendo Wii due to it also being able to play Gamecube games and offering older Nintendo games as downloadable content.
Actually they don't because they are REGION LOCKED. This means it can only play video games from the same country or region that it was purchased from. If you have a US bought console you will have to buy US/Canadian games. If you had a UK bought console you would only be able to play UK games.
Yes, you can still download games Virtual Console games from the Wii shop and play it on the Nintendo Wii.
Yes, the Nintendo 2DS is compatible with 3DS games. However, autostereoscopic 3D will not function.
Yes United States Nintendo DS games can be played on a Nintendo DS UK console. This is because DS games are not locked according to PAL regions.