Specifically iPhone/iTouch, Droids, and the new Windows Phone 7? I don't know how to quantify this, or if any research has been done. I am wondering how important the music is to the gaming and what % of games come with music at all, if good music at that.
I wouldn't say music is critical, but good music on any platform can greatly enhance the player's experience. The most important consideration with respect to music is that the music be appropriate--it should fit the game, and it should be somewhat subtle; it should not be too distracting. I would argue that poorly chosen music can easily be worse than no music at all, so it's worth investing time (and often money) to put together a good soundtrack. Your soundtrack should be large enough that it does not become too repetitive, and there must be a way to adjust the volume and switch the music on/off entirely (this functionality is usually provided for you in mobile devices).
If securing a proper soundtrack is not a viable option for you, then consider subtle ambient background sounds instead (see Angry Birds for an example).
I have no meaningful figures about the percentage of mobile games shipping with music, but most of the games I've played do include music, or at least ambient background sounds. There are some notable exceptions of excellent games without music, including Trainyard on the iPhone, which easily ranks in my Top 10 favorite mobile games.
The perception of audio quality usually is a plus or minus to overall game quality perceived. Generally most good audio is not spotted by the user, but their perception of game quality is increased.
Also consider that music themes and characterized sound effects are quickly recognized and can quickly become a symbol for a game. Music is a very strong IP like a strong character, and leaves its traces even hearing once. A good music, when switched off later, will continue playing in people's head while playing the game, and later also while not playing the game.
We recently published a puzzle game with minimal sound design with no music and received plenty of comments asking why the game has no music and should have one. In addition to that, although the sound design was minimal but careful, we have also seen people using headphones to play the game instead of turning the sound off.
Considering the fact that it is usually very hard to get feedback on audio (unless it is really bad or have great emotional songs), and experiencing people asking for music and preferring headphones even for minimal designs, music is quite important for all games. Game developers shouldn't underestimate its potential for mobile games.