For the most part, the people surrounding the Hebrews took little interest in them for much of Hebrew history. The Hebrews themselves don't actually appear in history until the reign of Marniptah, king of Egypt from about 1224-1211 BC. The son of Raamses I (1290-1224 BC), generally taken to be the king of Egypt at the time of the Hebrew exodus, Marniptah undertakes a military campaign in Asia in 1220 BC. In an account of the campaign inscribed in granite, a list of all the conquered peoples includes the Israelites who are mentioned as "now living in Canaan."
Before this point, the only history of the Hebrews we have are written by the Hebrews themselves, in Genesis 12-50. In the Hebrew account of their own history, they trace their origins back to a single individual, Abraham, who comes originally from Mesopotamia. The histories of the pre-Egyptian Hebrews is generally called the age of the patriarchs (patriarch means "father-ruler"); while it is virtually impossible to date this age since a.) the Hebrew history of the age is written down after more than a thousand years had passed and b.) no-one else was interested in the history, scholars place this age roughly between 1950 and 1500 BC.
Several aspects emerge from this history. First, the history of the patriarchs indicates that the special election of the Hebrews, made manifest in the delivery from Egypt, begins before the Egyptian sojourn and delivery. In Hebrew history, Abraham and his descendants are selected by Yahweh to be his chosen people over all other peoples. Abraham, who is a Semite living in Haran, a city in northern Mesopotamia, and whose father, Terah, comes from the city Ur in southern Mesopotamia, is visited suddenly by Yahweh and told to move his family. If Abraham's migration can be dated to around 1950 BC, this means that his migration from Mesopotamia would make sense, since the region was collapsing into chaos. Migrating to the west, Abraham stops at Shechem and is again visited by Yahweh, who then tells him that all this land will be given to him and his descendants. So the election of the Hebrews involves a certain unexplained quality (why pick Abraham) that is partially answered by Abraham's unswerving obedience when Yahweh asks him to sacrifice his son. But more importantly, the foundation of the Hebrew view of history is contained in these patriarchal stories. God ("Elohim" in Hebrew) has a special purpose in history and has chosen the Hebrews and the Hebrews alone to fulfill this purpose. In order to fulfill this purpose, God has entered into a covenantal relationship with the Hebrews and promises to protect them as a lord protects his servants. As servants, then, the principle duty that Abraham and his descendants owe to god is obedience.
The second aspect that emerges is that the early Hebrews are nomads, wandering tribal groups who are organized along classic tribal logic. Society is principally organized around kinship with a rigid kinship hierarchy. The relationship with god is also a kinship relationship: anybody outside the kinship structure (anybody who isn't a descendant of Abraham) is not included in the special relationship with God. At the top of the kinship hierarchy is a kind of tribal leader; we use the Greek word, "patriarch," which means "father-ruler." Well into the monarchical period and beyond, the Hebrews seem to dynamically remember their tribal character, for Genesis associates civilization with Cain and his descendants (meaning that civilization is not a good thing) and the history of the monarchy is clearly written from an anti-monarchical stance, since it is made clear that desiring a king is disobedience to God.
The third aspect that emerges is that these tribal groups of early Hebrews wandered far and wide, that is, that they did not occupy the lands around Palestine; this occupation would come considerably later. They seem to freely move from Palestine, across the deserts, and as far as Egypt. At several points in the narrative, Hebrew tribes move to Egypt in order to find a better life. It would not be unfair to imagine that the Hebrews were among the infinite variety of foreigners who overwhelmed Egypt at the end of the Middle Kingdom.
Beyond this it is difficult to come to certain conclusions. As far as the religion of the early Hebrews are concerned, it is generally believed that it had nothing to do with the Yahweh cult which is introduced by Moses, for Exodus asserts that Moses is the first to hear the name of god, Yahweh. The Hebrew accounts of the patriarchs generally use the term "Elohim" (God), "El Shaddai" (God Almighty), and other variants. Several religious practices described in Genesis seem to indicate a belief in animistic forces and even, possibly, polytheism, but these passages are highly controversial.
All we know for certain is that by the end of the patriarchal age, several tribes identified with one another as having a common ancestor and a common identity. We don't even know what they called themselves; we haven't successfully figured out where the term "Hebrew" comes from, although the best guess is that it comes from the Egyptian word, "apiru," or "foreigner." Several members of these tribes, whatever they called themselves, at some point migrated to Egypt, and Egypt would be the crucible in which would form the people and nation of Israel.
Sources: The Hebrews: A Learning Module from Washington State University, ©Richard Hooker, reprinted by permission.