Moses supposedly lived in Egypt for about 40 years and then fled for about 40 years before being in the Desert for about 40 years.

Leviticus 12:

1 The LORD said to Moses, 2 “Say to the Israelites: ‘A woman who becomes pregnant and gives birth to a son will be ceremonially unclean for seven days, just as she is unclean during her monthly period. 3 On the eighth day the boy is to be circumcised. 4 Then the woman must wait thirty-three days to be purified from her bleeding. She must not touch anything sacred or go to the sanctuary until the days of her purification are over. 5 If she gives birth to a daughter, for two weeks the woman will be unclean, as during her period. Then she must wait sixty-six days to be purified from her bleeding. 6 “‘When the days of her purification for a son or daughter are over, she is to bring to the priest at the entrance to the tent of meeting a year-old lamb for a burnt offering and a young pigeon or a dove for a sin offering.[a] 7 He shall offer them before the LORD to make atonement for her, and then she will be ceremonially clean from her flow of blood.

“‘These are the regulations for the woman who gives birth to a boy or a girl. 8 But if she cannot afford a lamb, she is to bring two doves or two young pigeons, one for a burnt offering and the other for a sin offering. In this way the priest will make atonement for her, and she will be clean.’”

7+33=40 days, 14+66=80 days.

See also the spies (40 days), Noah waiting to open the Ark (40 days), and more here.

The "embalming" is an interesting inclusion because it tells of an Egyptian practice, which might stem from the same cultural idea of 40 days/years being a complete unit or is a projection onto them, or be a transcription of an idea directly into metaphor, (nearly) ignoring the literal truth of how long it took, or be erroneous projection. Genesis 50:

1 Joseph threw himself on his father and wept over him and kissed him. 2 Then Joseph directed the physicians in his service to embalm his father Israel. So the physicians embalmed him, 3 taking a full forty days, for that was the time required for embalming. And the Egyptians mourned for him seventy days.

4 When the days of mourning had passed, Joseph said to Pharaoh’s court, “If I have found favor in your eyes, speak to Pharaoh for me. Tell him, 5 ‘My father made me swear an oath and said, “I am about to die; bury me in the tomb I dug for myself in the land of Canaan.” Now let me go up and bury my father; then I will return.’”

6 Pharaoh said, “Go up and bury your father, as he made you swear to do.”

7 So Joseph went up to bury his father. All Pharaoh’s officials accompanied him—the dignitaries of his court and all the dignitaries of Egypt— 8 besides all the members of Joseph’s household and his brothers and those belonging to his father’s household. Only their children and their flocks and herds were left in Goshen. 9 Chariots and horsemen[a] also went up with him. It was a very large company.

10 When they reached the threshing floor of Atad, near the Jordan, they lamented loudly and bitterly; and there Joseph observed a seven-day period of mourning for his father.

I included the full length of that so no one says "Aha! Apparently the writers were willing to say '70 days' when something took that long, so the 40 is not a metaphor." Consider that the other mourning period is a multiple of 7.

In a word: yes, it uses it all over the place. I believe also in the original Hebrew for the OT; I don't know anything about the NT. I was going to list some examples, but you can grep the Bible just as well as I can.

EDIT: Oh, I misread your question. Gimme forty seconds to go look.

RE-EDIT: 40 years in the wilderness.