Since I got the Wii in 2008, I've played only about half of the games I own for it with motion controls. For the games that are compatible with more than just motion controls, I always choose the other control options because it fits my preference and/or situation more. As far as control goes, the Wii is more flexible out of the box than XB360 or PS3. Nintendo makes a plethora of control hardware for developers to utilize; Wii remote (motion-control wand with design similar to NES controller), the Classic Controller (design similar to other Nintendo controllers), Classic Controller Pro (design similar to Sony controllers), GameCube controller (almighty), Wii wheel (typical arcade game steering wheel design), Zapper (arcade gun game design)...and the Wii is set for them right out of the box. It's just great being able to choose form different types of stock control hardware to suit different types of games.
To start, the Wii Remote itself can be used in a number of different ways; sideways (like the old NES controller) for MegaMan 9, as a point-and-click(er) for Zack & Wiki, with the "numb-chuck" attachment for tag-team combo smashing in SpyBorgs, or as a homerun hitter in Dead Rising - Chop Til You Drop. Then, you got the Classic Controller for Tatsunoko VS Capcom, the Classic Controller Pro for Sengoku Basara: Samurai Heroes, and the Zapper everyone loves for Resident Evil: Umbrella Chronicles. Even now with the Wii in its later years, side-scrolling brawler Spyborgs arguably represents perfectly-implemented motion controls, with maneuvers that make sense and aren't awkward. Perfectly-executed, innovative control (for the genre) is one of the reasons SpyBorgs is not only my favorite Wii title, but probably my favorite overall title for its generation. Unfortunately, however, some games aren't developed this well with motion controls, and the Wii's control freedom has that variable covered. If one control type doesn't work for you on a certain game, you can always try another. Resident Evil 4 - Wii Edition is the best example of this. Though the game was advertised with Wii Remote controls and marketed accordingly, the game is actually compatible with the Classic Controller and the GameCube Controller! Critics will ask why "anyone would want to play it without motion-controls," but it's the options here that really count because it opens the game to an even wider audience. Newcomers or those who like challenging control may prefer the motion controls, but there are also RE4 veterans would prefer to experience the new Wii Edition additions with control familiarity. I'm one of those veterans, and greatly thankful for Nintendo making the Wii controls so flexible that Capcom was able to provide three control types to make the game as accessible as possible.
Alternate controls are also good for people like me who live in smaller homes with not as much room. Some say the "essence" may be gone, but still, even people with smaller homes should be able to enjoy the same games, too. There's no reason why someone shouldn't be able to enjoy a masterpiece like RE4WE simply due to motion-controls. Not only that, but everybody has those days where they just want to come home after a tough day at work (or the gym) and unwind with some gaming. Maybe they want to enjoy a video game, but are too tired for swinging and flailing. Alternate controls allow for the owner to switch control types if they need to, depending on situation or mood. As always, Nintendo was ahead of the curve with this concept, and it will continue to influence future development. Well, that and the decline of arcades, but we'll save that one for a rainy day...