Cut the Rope HD
Besides winning a handful of game industry awards, "Cut the Rope," a Chillingo game developed by ZeptoLab, was the first Apple iOS game to win an award from the British Academy of Film and Television Arts. In the game, you work with on-screen objects and laws of physics to feed a small green animated character named Om Nom.
"Cut the Rope HD Lite" is free with 18 levels, but an upgrade to the paid version for $2.99 gets you a full 200 levels.
"Cut the Rope" has fun music and sound effects, but they aren't essential to playing the game. This is true with similar animated games, including the immensely popular "Angry Birds" franchise and the more recent "Roll in the Hole HD." So, you can enjoy hours playing these games noise-free. Look for your in-game options to mute the music and sound effects of the game.
The final game on our list has become widely popular on a variety of mobile platforms, and noise-free is no problem for game play.