The most common mold to grow on most any fruit, including apples, is penicillin mold. It is fuzzy and white at first, turning dark as it matures. Fruit is a good source of the moisture mold requires to grow.
Definitely. An apple that's been cut open and left to rot will grow mold- normally a blackish color. Also it can get moldy if you leave it in your fridge for too long and forget about it- normally a whitish color. But by that time, the apple would be soggy and gross in both cases.
