The DS touch pad and 3DS screen are where they've innovated in hardware outside of the Wii most recently. There's other smaller things like GBA linking up to the Gamecube for a variety of things and the wireless adapter that came with Pokemon Fire Red and Leaf Green. I can name things like analog sticks, rumble and the SNES pad design (and Wiimote design) which were subsequently stolen directly by Sony and still being used, but yeah, I generally think Nintendo's pretty good when it comes to innovating.
In terms of software, I guess going by the highest selling ones that I think innovated entirely I'd point out Wii Sports, Wii Fit, Nintendogs and Brain Age. Whether you want to count titles like Cooking Guide, Style Savvy, or Art Academy is up to you. I could mention some games they've made such as Donkey Kong Jungle Beat that came with a bongo drum, or mention regular games that have innovated in the tradtional gameplay sense without becoming a ridiculous phenomenon or requiring extra hardware, but that's not really important. AR games from the 3DS are going to be big but considering Sony's NGP has it covered can't really credit Nintendo for that.
Do you make a distinction between Wii casuals and people who play on iPhone or Facebook? I don't. Let's imagine that anyone playing games on those platforms will never try other types of traditional games no matter what, how would that be bad for the industry? People will be employed to create those specific games to cater for that audience. Having more people being employed making games, more businesses making money and more people overall playing games, no matter what type of games, sounds like it'd be a benefit for the industry rather than a detriment. And yeah in terms of who's benefitting the industry the most right now you can look at those 3 names listed above, followed by Microsoft. More people spending money inside an industry is never a detriment. HD console games costing 50+ million have hurt the industry, if you need any proof ask the dozens of studios that have shut down.
But of course pretending that people who started playing games waggling remotes, jumping in front of screens or farming crops won't move onto other types of games is ridiculous. You can look at sales figures, surveys and attach rates to figure out if these casuals are buying other games, and they are. No one's claiming all of them do, but a significant portion do if there are games being released at a steady pace.
And that's why Nintendo is shifting their focus from creating motion control games to 2D platformers, which they said at E3, citing Mario Kart Wii as a "bridge title" that's an example of casual users moving onto more core oriented games. Mario Kart Wii and DS didn't sell 25+ million copies on other systems. Mario Bros. Wii and DS didn't sell 25+ million on other systems. Who bought the extra 20 million copies that Double Dash didn't sell? The anomaly in gaming is why people think those extra 20 million copies came from thin air. And if you look at the sale charts, those games are always selling. That's the greatest thing about the Wii and DS, because those are core games selling to brand new people. People can do a lot worse than starting with 2D Mario and Mario Kart, I'll tell you that. Nintendo is specifically determined to make casual Wii and DS owners move onto more core titles, and why wouldn't they, it's good business sense.
Motion controls are simply an easier interface. Once the interface is conquered, which was the main barrier to entry, people who were previously against playing any type of games will naturally become more open to other types of games simply by owning the machine. It's not rocket science. People bought Wiis for motion controls, no doubt about it, but who bought Mario Kart? Mario Kart Wii should have sold 5 million like Double Dash, but it's sold 25+ million and still going. An anomaly is right~