A controller might not be necessary, but for anyone that plays slightly more involved games than iOS has, it's a godsend. Playing a platformer on an iPod touch is rather annoying.
Some titles have. It doesn't work out as well as you might hope; those inputs aren't exactly precise, and tilting the screen can be a bit disorienting. The result is that level layouts have to be much simpler to maintain the same degree of challenge.
Thanks. I have played the new Super Mario Bros. on the Wii. They make use of shaking and tilting the controller, but very sparingly and buttons are the main means of control.
(It's a good game. I was expecting it would follow the trend of making games ever more casual. I was wrong. Mario Bros. Wii is hard.)