“The three systems of divination which we have analyzed all entered directly into the religious life of the people and illustrate some of the religious practises which were maintained, like the incantation rituals, throughout all periods. The longing to pierce the unknown future, to pull aside the veil which separates us from a knowledge of coming events, is so strong in man as to have all the force of an innate quality an instinct of which he himself only gradually becomes fully conscious.
It plays an unusually prominent part in the religion of Babylonia and Assyria, indeed so prominent as to justify us in asserting that by the side of the ever present fear of the demons, the significance attached to omens was the most conspicuous outward manifestation of the religious spirit of the people taken as a whole.
This conclusion is strengthened by the knowledge that we now have of other forms of divination, such as pouring a few drops of oil into a basin of water, and according to the action of the oil in forming rings and bubbles that sink and rise and the directions in which they spread, conclusions were drawn of a more or less specific character, and suggested by a more or less artificial association of ideas with the action of the oil bearing either on public affairs or on private matters, according to the questions asked of the diviners, to which they were expected to give an answer. 
Within the other category of involuntary divination where the sign is obtruded on your notice, falls the importance attached to dreams, the interpretation of which formed in fact one of the most important functions of the Babylonian-Assyrian priests acting as diviners. References to dreams are frequent both in the older and later inscriptions of Babylonian and Assyrian rulers. 
A majestic figure reaching from earth to heaven appears to Ghidea in a dream ; it turns out to be the god Ningirsu. A female figure also rises up with a tablet and a stylus who is the goddess Nisaba.
The sun mounting up from the earth is explained to be the god of vegetation, Ningishzida. Various utensils and building material and an ass to carry burdens which the ruler sees in his dream leave no doubt as to the interpretation of the vision. It is the order to Gudea to build a temple according to the plan drawn on a tablet by a second male figure appearing to him, and who turns out to be the god Nin-dub. The interpretation is given to the ruler in this instance by the goddess Nina as whose son he designates himself.
Ordinarily, however, it is to a priest to whom rulers and people go to learn the meaning of dreams, in the belief that dreams are omens or signs sent by the gods as a means of indicating what is about to happen ; and even in Gudea’s case we may safely assume that the interpretation ascribed to the goddess directly was furnished to him through the mediation of the priests.
At the other end of Babylonian history, we find Nebuchadnezzar and a goddess appearing to Nabonnedos, the last king of Babylonia, in dreams to explain certain strange signs that had lately been reported. In the inscriptions of Ashurbanapal, the great king of Assyria, there are several references to dreams.”
Morris Jastrow, The Civilization of Babylonia and Assyria, 1915, pp. 266-7.