The Wii has obviously expanded the market. You only need to look at hardware sales. A console doesn't sell with those sorts of astronomical numbers without enticing some new fish.
In terms of controls, Lukasz is spot on. The Wii Remote and Nunchuck set-up has helped numerous genres - to add to the examples he already gave, several kinds of sports games, namely football (soccer) and golf, have benefited strongly. I also feel that quirky concepts, particularly the ones from the imagination of indy developers, are much more at home on the Wii platform. WiiWare has been a stellar opportunity for those ideas; a lot of the good games both currently out and upcoming for Nintendo's new download front would only work with the motion and pointer functionality given by these controllers.
Pedro brings up a good point that there are still potential types of videogames to tap into on Wii successfully. What I immediately thought when I read that was real-time strategies. It has primarily been a PC genre since it began and whenever someone has attempted to replicate it on consoles, it wasn't really a worthwhile endeavour. The IR pointer on the Remote could change that. As highlighted before, it could provide the same speed and precision that a mouse offers, which is essential for the micro-management needed in a RTS that dual analogue has failed to do all that well. Unfortunately, nobody has bitten the bullet and tried it out on the Wii yet, except for Kuju with Battalion Wars II, which plays quite differently to your usual strategy title.
Another good feature, enjoyable to read. It must be tough to think up new ideas, organise everyone and then edit everyone's responses in a sensible order, so I appreciate what you're doing, James.