As suggested by David, the Mari documents are of no help in substantiating the wanderings of the Exodus period. The Amarna letters, found in the Egyptian city of Amarna, are helpful because they provide valuable information about conditions in the Egyptian empire during the middle of the 14th century BCE. 1 Kings 6:1 places the Exodus from Egypt approximately 1440 BCE, because this verse dates the Exodus 480 years before the fourth year of Solomon's reign, and the Bible implicitly dates this year of Solomon's reign at 960 BCE. The existence of the Amarna letters, in which the Canaanite kings are preoccupied with petty squabbles amongst themselves, shows that any Israelite military conquest of the Canaanite cities must have occurred much later than, say, 1350 BCE.
They are a reliable extra-Biblical sources, because of their existence in an abandoned Egyptian city where their contents were not subject to forgery or alteration. The letters do not tell us anything about the account found in Exodus of the Israelites wandering in the desert, apart from demonstrating that the Exodus must be dated much later than previously supposed. They contain background information not included in the biblical account and which could be useful in interpreting it, in that the continuing Egyptian presence in Canaan is contrary from what we would expect from reading the Bible, and because the Canaanites of that time relied on the Egyptian army for defence rather than on high city walls.
As for the Egyptians losing documents that didn't paint them in a good light, it is true that most Near Eastern kingdoms did tend to gloss over their failures. However, the Egyptians could not have hidden the economic impact of a series of plagues, the loss of a very substantial slave population or the destruction of an entire army in the Red Sea. Substantial numbers of documents, including routine commercial documents and contracts show that Egyptian society continued unaffected by the biblical events reported in the Book of Exodus.