I would venture to say that the vast majority of moats - also commonly referred to as ditches - were dry, and that wet moats were the exception, not the rule. This is because connecting a ditch to a water source is an additional hassle, and one that may be avoided without much reduction in the protection provided.

Dry ditches are an exceptionally ancient type of fortification. Examples abound going back into literal prehistory. Whether the Iron Age forts of Celtic Britain, Roman fortifications throughout Europe, Africa, and Asia, or the burgs of Alfred the Great, ditches were extremely widespread throughout the ancient and medieval world. A steep-sided ditch fifteen or twenty feet deep, dug in the shadow of an earthen berm, or more expensively a timber or stone wall, is a formidable obstacle to any attacking force. Think about trying to descend such an embankment while burdened with weapons and armor, perhaps carrying a scaling ladder, and then ascending the other side, all the while you are being pelted with arrows and javelins. That you don't have to worry about water is small consolation indeed.