There is more information about Moses Cleveland than is sometimes available,because he left more records than some immigrants, and because he is the ancestor of Grover Cleveland and thus has been pretty thoroughly researched. Still, I haven't seen documentation for his birth and there are varying guesses as to his parents.
My favorite candidate for his parents would be Isaac Cleveland and Alice, last name unknown. They were in Ipswich, Suffolk, England, which is generally given as Moses' birthplace, and they were of the right age to be his parents. In addition, there is the Biblical name tradition, as it appears. Other suggestions I have seen were for a Samuel Cleveland, but I don't think he was from Ipswich.
There is an absolutely fascinating story about Moses's voyage to America, but it may well be just that-a story. Still, on the off chance that it's correct, the story goes that when Moses came to America, he had thought it would be Virginia rather than New England. The story goes that when they landed at Jamestown, the group after a short time decided there was too much trouble with the native Americans, and boarded the ship to go to Massachusetts instead. There is much that is suspicious about this story but it could have happened.
At any rate, young Moses, no more than fifteen, arrived at Plym. outh or Boston in 1635. He was a ship's carpenter apprentice when he arrived, He seems to have stayed in Boston for about three years, then in 1638 he settled in Charlsetown.
He was still serving a master, probably Edward Winn, when he went to Woburn in 1640 or 1641, but was admitted a freeman in 1643, He was granted land in 1649, and on February 3,1648/1649 was appointed by a committee to lay out his own land. He married Ann Winn, daughter of Edward Winn, in 1648 and the couple had at least eleven children. The first is listed with a birthdate of 1651 so it's possible there were miscarriages or still born children in the early years of their marriage.
Moses was a joiner, or basically a finish carpenter, and worked both on ships and on homes. This gave him an income sufficient to support his large family. He is listed on the militia roll in 1663. A later listing for Moses Cleveland during King Philip's War is more likely his son Moses. He became a tithing man for the church in 1680, so he was a Puritan. He died in Woburn on January 8, 1702, having lived there for 60 or more years, and having survived his wife by about 20 years. It isn't often that our ancestors stayed in one place for a long time so I would like to thank Moses for doing just that!
The line of descent is:
Moses Cleveland-Ann Winn
Enoch Cleveland-Elizabeth Counts
Sarah Cleveland-Israel Joslin
Sarah Joslin-Edward Fay
David Fay-Mary or Mercy Perrin
Luceba or Euzebia Fay-Libbeus Stanard
Hiram Stanard-Susan Eddy
Louis Stanard-Mary Alice Hetrick
Etta Stanard-Loren Holbrook
Gladys Holbrook-Richard Allen