What are some similarities and differences of the religious beliefs between the Mesopotamians, Egyptians, Hebrews, and Assyrians?
The most obvious similarities involve the belief in one (or more, in the case of all but the Hebrews) deities, and a belief in an afterlife. The most obvious difference, of course, is the monotheism of the Hebrew religion.
The early Mesopotamian religions, like almost all mythologies, portrayed the actions of nature as those of gods and goddesses. These were brought into being by four creator gods, who were in turn created by Taimat and Abzu, personalized (or anthropomorphized, if you will) forces which arose from a primordial chaos. There was a sky-god, An, Enlil a storm/weather god, an earth god named Nin-khursag and a water god named Enki. You see the same or variations of these and other lesser gods and goddesses throughout Mesopotamian history from the earliest cities through the great empires of Babylon and Assyria. Sumerian culture being Mesopotamian the same basic beliefs apply- a flat earth surrounded by seas from which the universe arose, the sky-god An and the goddess Ki giving birth to Enlil, etc.
The religion of Israel is the dramatic difference from others which arose in the area. Of course, according to the Holy Bible ("Separated Book") this monotheistic religion was the original religion and the others were ideas which came later due to superstition and ignorance. The creation myths of Babylonian culture and that of the Bible are quite similar except in this one point, and Oxford professor Dr. Stephan Langdon in Semitic Mythology claimed that his study of the earliest Babylonian inscriptions led him to conclude that the original religion of the area had indeed been monotheistic, and polytheism came later. The Bible states that Abraham, father of the Arabs and Israelis, came from the Babylonian city of Ur, a city in which a moon-god cult was predominant. The Hebrew religion differs in the concentration on a history of one family running from the first humans through Abraham and his descendants to an eventual "anointed" who would release mankind and the physical world from the burden of the human propensity for wrong-doing once and for all. All these religions (including Israel in the meantime) used animal sacrifice (or human, for some of them).
Egyptian religion was similar to those of Babylon and Assyria; there was an watery chaos called Nun, out of which came the creator Ra. Ra incidentally has three aspects- in the morning Khepera the Creator, at noon Ra the Sun-god and in the evening Atum the Complete. Ra also had a secret name. The Egyptians had a set of gods and goddesses with personal relationships which gave form to their complex religion, the core of which was contained in the well-known Book of the Dead. This "book" was a set of murals in hieroglyphics which would be painted on the inner walls of the tombs of the rich and powerful to guide their spirits through the ordeal of judgement in the afterlife.
Early Mesopotamian religions, later versions throughout the area, the Israeli religion and Egyptian all believed in life after death, and the latter two in a judgement of the soul of the deceased based upon actions and beliefs during life. Most Mesopotamian religions did not believe in a chance of paradise after death, but simply an unending second life of a rather dismal sort.