Moses is, arguably, the most significant prophet in Judaism and is credited with leading the enslaved Jewish population out of Egypt and into the promised land.
Aside from the Torah, are there any verifiable records or concrete evidence that there was an actual Moses? Is he mentioned at all by the Egyptians during the exodus, or cited by other cultures or religions?
There is no direct evidence, outside of the Torah and the literary traditions which followed, that Moses ever existed. Whether he was made up out of whole-cloth, or whether there is some historical basis behind the legend, is impossible to say. The best you can do is consider that:
Extensive archeological surveys throughout the Sinai region seem to have thoroughly discredited the possibility that any population movement as massive as the Exodus described in the Torah ever occurred. (See xiaohouzi79's answer for references)
Some details of Moses' life seem to have been lifted from earlier legends; specifically, the idea that his mother placed him in a basket and floated him down a river is reminiscent of a legend involving Sargon of Akkad. See Pritchard, J. "Ancient Near Eastern Texts Relating to the Old Testament", Page 119
Specifically, in the legend of Sargon it is written that "my mother, the high priestess, bore me in secret. She set me in a basket of rushes, with bitumen she sealed my lid. She cast me into the river..."
Compare this with Exodus 2:3 (NIV): "But when she could hide him no longer, she got a papyrus basket, for him and coated it with tar and pitch. Then she placed the child in it and put it among the reeds along the bank of the Nile."
Note, however, that it is not necessarily the case that the Hebrews lifted the basket motif directly from this Akkadian legend, as the earliest known copy of the Akkadian legend dates to after the time the relevant passage in Exodus was probably written (8th century B.C.E). However, it is likely the legend about Sargon comes from earlier, Babylonian sources.
While there is no direct evidence that the Hebrews were ever enslaved by the Egyptians, there is evidence that Semitic slaves were kept in Egypt, however the texts which prove this date to 600 years before the generally accepted date of the Exodus (~1200 B.C.E). See "Asiatics in Egyptian Household Service" from Pritchard, J. "Ancient Near Eastern Texts Relating to the Old Testament", Page 553
This document records the names of various slaves in service in Egyptian households, including one Menahem, which was later a common Hebrew name, as well as the name of a Hebrew king. Another slave name is "Sephra", which is etymologically similar to the Hebrew name "Sapphira".
This doesn't prove that the Hebrews were enslaved as described in Exodus, however it does demonstrate that it wasn't anything out of the ordinary for Semitic peoples to serve as slaves in Egypt (especially before the Hyksos period). It is therefore possible that the Exodus story has some kernel of truth to it, even if it has been exaggerated beyond recognition.
Of particular interest is Papyrus Anastasi V (British Museum 10244), dating to around the time of the Exodus, (13th century B.C.E), which records a correspondence regarding the pursuit of two runaway slaves. See Pritchard, J. "Ancient Near Eastern Texts Relating to the Old Testament", Page 259
It is notable because the route taken by these slaves took them past the watchtower at Migdol, which is the same route mentioned in Exodus, where Moses led the Israelites before stopping in front of the sea. (See Exodus 14:2-3)
None of this comes even close to giving us direct evidence that the Exodus occurred or that Moses himself even existed. However, it does demonstrate that the Exodus account may be based on one or more (much more mundane) historical incidents, which are now permanently intertwined with later mythological embellishments.
Short answer: there is no historical evidence of Moses' life outside of Israelite texts.
Perhaps an appropriate question you didn't ask is should we expect there to be evidence of Moses outside of the texts of ancient Israel? If the stories are false, obviously we would not. If the stories are true, there is good reason to expect other ancient civilizations would not be interested in recording them either because they represent defeat or because they were irrelevant to them.
Among the first category would be the Egyptians who according to the Torah lost a large pool of labor, significant military power, various crops and herds, and every first-born son. It would have been a complete humiliation and a blot on the current pharaoh's name. Assuming such an event were ever recorded, it seems unlikely that the record would be as widely copied as a major victory. (In this sense at least, history really does belong to the victor.) Similarly, the Canaanite peoples who were displaced by the Hebrew people would not be interested or even able to record their own defeat.
In the later category would be the vast majority of the rest of civilization for whom even such a remarkable event as the Exodus would be a minor rumor at best. According to it's own history, Israel was only relevant internationally for the short period of monarchy culminating in the reign of Solomon. Deuteronomy emphasizes the insignificance of the Hebrews at the time:
It was not because you were more in number than any other people that the Lord set his love on you and chose you, for you were the fewest of all peoples, but it is because the Lord loves you and is keeping the oath that he swore to your fathers, that the Lord has brought you out with a mighty hand and redeemed you from the house of slavery, from the hand of Pharaoh king of Egypt.
Therefore, it would be somewhat surprising if we found evidence of the Exodus outside of the Hebrew records. And if the Exodus story were not recorded, then there's no reason to expect the life of Moses to be recorded either.
Tellingly, the earliest extra-Biblical evidence we have that such a people as Israel exists comes as a brief mention of their defeat and extermination (declared prematurely as it turns out) at the hands of Merenptah, an Egyptian pharaoh. The relevant line translated reads:
Israel is wasted, bare of seed,
That is the sort of evidence we might expect outside of Hebrew sources. It's also typical of the records we have from the period: biased and self-serving. (Seriously, read the whole thing.)
The Torah is atypical of the period in that sense—it records both the victories and the follies of the Hebrew people and of Moses. Compared to most ancient rulers, Moses seems surprisingly human. Is that evidence that the Torah dates back to near the end of the events it claims to record? Of course not. But it's the sort of thing that makes dating the early Hebrew texts such an interesting puzzle.
For instance, the first story of Moses' adulthood is an account him murdering an Egyptian:
One day, when Moses had grown up, he went out to his people and looked on their burdens, and he saw an Egyptian beating a Hebrew, one of his people. He looked this way and that, and seeing no one, he struck down the Egyptian and hid him in the sand. When he went out the next day, behold, two Hebrews were struggling together. And he said to the man in the wrong, “Why do you strike your companion?” He answered, “Who made you a prince and a judge over us? Do you mean to kill me as you killed the Egyptian?” Then Moses was afraid, and thought, “Surely the thing is known.” When Pharaoh heard of it, he sought to kill Moses. But Moses fled from Pharaoh and stayed in the land of Midian.
Another oddity of the Torah that doesn't prove anything, but is a puzzle for those holding a late date for it, is that the city of Jerusalem is not mentioned. It isn't until David is said to move the royal residence from Shiloh to Jerusalem that the city is given any importance. The important center for the Hebrew patriarchs according to the Torah seems to be the city of Hebron. Given the reverence that Jerusalem is held in by the majority of Jewish texts, it's surprising that the city remains unnoticed in the Torah. But we are pretty far afield from the original question.
In summary: there is no independent evidence of Moses, there's no reason to expect any, but the evidence in the Torah seems unusual if read as myth and legend.
According to the Wikipedia article on Moses:
Prominent archaeologists and Egyptologists dispute the existence of Moses as well as the veracity of the Exodus story, citing logical inconsistencies, new archaeological evidence, historical evidence, and related origin myths in Canaanite culture.
Citing the following references:
Princeton University Press Press Reviews, retrieved 6th June 2009
The Quest for the Historical Israel: Debating Archeology and the History of Early Israel, 2007, Society of Biblical Literature, Atlanta, ISBN 978-1-58983-277-0.
John Van Seters, "The life of Moses", ISBN 903900112X
And further:
The tradition of Moses as a lawgiver and culture hero of the Israelites can be traced to 8th or 7th century BCE in the kingdom of Judah. Moses is a central figure in the Deuteronomist account of the origins of the Israelites, cast in a literary style of elegant flashbacks told by Moses. The Deuteronomist relies on earlier material that may date to the United Monarchy, so that the biblical narrative would be based on traditions that can be traced to about four centuries after the supposed lifetime of Moses.
