Here are some music games and Apps that I find interesting:
Smule Auto Rap:
Interesting app that reads voice input and turns it into auto-tuned rap like songs.
Smule Magic Piano:
A really fun way to "play" piano in a sort of music game. Nice simple art style. Also has a freestyle piano playing feature.
A kind of collection of all of smule's music performing apps.
Ok last smule one, I promise!!
Smule Magic Guitar:
A magic-piano-like app.
Ok now on to the iOS games:
Flea Symphony:
Interesting art style and game concept. Mostly rhythm focused, and not super musical in the end.
Groove Coaster:
Pretty addictive and fun game by the people that brought you space invaders. Simple but effective visual style, and game mechanic of just tapping the screen anywhere.
Tap Tap Franchise:
Rock Band-like game play, but it utilizes the accelerometer and swiping gestures. Again, like the previous examples, you're not really creating music, just playing it back.
Theatrhythm Final Fantasy:
Another iOS game themed to the Final Fantasy franchise. Nice art style, simple game play. Creative level up and character choosing RPG dynamics.