According to the Skeptoid episode (quoted above by @EdSG) and other sources, there is no archaeological nor historical evidence to support the biblical account of enslaved Israelites in Egypt, nor the Exodus story. According to Brian Dunning (Skeptoid), there are no Egyptian records of Jews or Hebrews having ever been in Egypt. The greatest of the pyramids, he continues, were completed 600 years prior to the settling of the land of Israel which he dates 1100 BCE. This is chronologically accurate.

This may or may not be entirely fair, though. While Brian is correct there was no Israel until this time, others would argue the nomadic ancestors of the Israelites may be considered Israelites even if not in name. Timelines and the Old Testament do not begin the story of the Israelites with the settlement of "The Promised Land." Support for this position is found on The Merneptah Stele (also known as the Israel Stele) from approximately 1300 BCE. The inscription (see below) reads "Israel is wasted, its seed is no longer."

Missing from this is the hieroglyph for "country," indicating "Israel" at this time referred to a people and not yet a country. Notwithstanding, some people called Israel were in the area and had a store of grain that could be "wasted." This does not, however, support either an enslaved people, nor a great wandering exodus: enslaved people do not have grain stores and nomads by definition do not have stores at all.

The Skeptoid podcast and other Egyptologists are generally correct. There are no Egyptian tablets, stela, nor inscriptions supporting the stories of enslavement nor physical evidence of the "Tribes of Israel wandering around the desert" (quote from Victor Stenger approximately 7 1/2 mins. into an interview with D.J. Grothe on Point of Inquiry).

This sentiment is repeated again and again: If you are looking for evidence of Israelites in Egypt and the desert, you will find no evidence in archaeology. "The only evidence that one might seriously consider is circumstantial." (From Amihai Mazar's The Patriarchs, Exodus, and Conquest Narratives section of The Quest for the Historical Israel: Debating Archaeology and the History of Early Israel). This circumstantial evidence requires elaborate gymnastics to line up known settlements with the Old Testament accounts;reminding me of attempts to fit recent events into centuries-old prophecy, like that of Nostradamus's quatrains. If the shoe doesn't fit, its not Cinderella; though it may be a fairy tale.