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Wikipedia says: "Here Ixx denotes the moment of inertia around the x-axis when the objects are rotated around the x-axis, Ixy denotes the moment of inertia around the y-axis when the objects are rotated around the x-axis, and so on."

So, when do you get a product of inertia(what's the rule)? I am guessing only when the rotating (about the center of mass) object has mass in regions x, y, z > 0. If one of the coordinates are zero and the object is stuck rotating in a plane, then I am assuming it has stable rotation?