Magicians like to use sponge balls for the same reason they like to use doves, playing cards, and spectators' money -- because they're cheap. Sponge balls are also quite versatile. You can vanish and produce them, crush and multiply them, flatten and transform them, even fry and eat them. They can be used in shows for children (as in the popular "Happy the Ball and her Multiplying Babies") or adults (for example, "Sponge Balls, Square Pants").
Because of their popularity, a number of devices have been invented specifically to facilitate magic with sponge balls. One such item is the sponge ball sleeve blower. This device, hidden in the sleeve and operated by a squeeze bulb in the magician's armpit, can blow sponge balls out of a sleeve into a magician's hand or suck them away -- even out of a spectator's hand -- in perfect silence. If you've ever seen a magician make a sponge ball disappear, then you've seen a sleeve blower in action.
Steel-core sponge balls are also popular. With a steel-core sponge ball and a powerful rare earth magnet hidden in a hollowed-out tooth, a magician is ready to perform a visually spectacular (although choking-risk intensive) "Sponge Ball Leap to Mouth" routine.
There are many more specialty sponge balls available to magicians, including ones that let magicians perform Pen Through Sponge Ball, Ambitious Sponge Ball, Sponge Ball Bite, Four Sponge Ball Assembly, Sponge Ball to Sponge Tiger, Vanishing Sponge of Liberty, and much more.