There can be found on the internet and in some secondary sources speculation that John Booth Scituate and Marshfield is related to various other Booth families in colonial America. There is no evidence to support any of this speculation. 
John Booth first appears in the records of Plymouth Colony in 1655, when he is granted land in Marshfield MA from the Winslow family, to whom he had been indentured. He married about Nov 1657 to Elizabeth Granger, daughter of Thomas and Grace Granger. Their children's births are recorded in Scituate, but it is believed the first three were born in Marshfield. He died between 1704 and 1709. He may have died at his son's home in Duxbury MA.
Born: About 1634.
Presumably had just recently turned 21 when on 18 May 1655 Josiah Winslow sponsored him for a land grant in Marshfield.
Marriage and Children
Married: (probably) November 1656 in Marshfield. Massachusetts.
On the first page of the original Marshfield records is a record which reads
"[worn]th & Elizabeth [worn] were married [worn] November 1656."
A comprehensive search found no other possible matches of a groom with a surname ending in 'th' and bride Elizabeth - this is almost certainly the marriage record John Booth.
Children of John Booth and Elizabeth Granger:
First three probably born at Marshfield.
Elizabeth Booth, born 5 October 1657. Died before 21 October 1709.
Joseph Booth, born 27 March 1659. Married 1st Frances Cowdrey; married 2nd Elinor Hethard. Died between 19 March 1633[/4? ]and 6 January 1736.
John Booth Jr. Born 1 January 1661/2.
Benjamin Booth. Born 4 July 1667.
Mary (Booth) Barden. Born 6 June 1669.
Abraham Booth. Born 7 February 1673/4.
Grace (Booth) Pray. Born 4 July 1677 in Scituate.
Judith (Booth) Peirce. Born 13 March 1680/1 in Scituate.
21 Feb 1698/9 John disposed of his property by three deeds of conveyance to his sons John Jr, Benjamin and Abraham. There was no deed for son Joseph. Joseph had been found guilty of fathering an illegitimate child in 1687 and shortly after left Plymouth and moved to Delaware (part of Pennsylvania). Each of the three deeds contained clauses that the said sons were to make cash payments to John's daughters, Elizabeth Booth, Mary Barden, Grace and Judith Booth. A deed 21 Oct 1709, mentioning "our father John Booth now deceased" further identifies the children: Joseph Booth of County Kent, Pennsylvania, Benjamin Booth of Scituate, Abraham Booth of Duxborough, Abraham Barden of Middleborough and Mary his wife, Ephraim Pray of Scituate and Grace his wife, and Isaac Pearse of Scituate and Judith his wife.
The 1698/99 carried the phrase that his wife acknowledge the deed, but evidently not so for about a year after John Jr's death she reversed some of the gift to John and gave it to Abraham stating she had not acknowledged the original deed. Elizabeth probably died before 1 May 1721 when Abraham signed a quitclaim reversing what his mother had done and restoring the property to John Jr's widow Mary.
Died: Between 2 August 1704 and 21 October 1709. 
Last known living on 2 August 1704 when he acknowledged a deed.
Dead by 21 October 1709 when his heirs signed a settlement deed.
The first record of him in New England was on 18 May 1655 Josiah Winslow sponsored him for a land grant in Marshfield. He did not actually receive this land until 1666. Young speculates he came to New England in 1644 as a servant to Gov. Winslow on one of the governor's return trips from England. 
↑ Young, Malcolm A. "John Booth of Marshfield and Scituate, Massachusetts: Servant and Planter." New England Historical and Genealogical Register 159:227-229 Link at AmericanAncestors ($) (article begins 220)
Young, Malcom A. "John1 Booth of Marshfield and Situate, Massachusetts" Servant and Planter." New England Historical and Genealogical Register, vol. 159 no. 3 (July 2005): 220-234. AmericanAncestors.org (by subscription)
History of Scituate, Massachusetts, from its First Settlement to 1831, Samuel Deane, (Boston: James Loring), pg. 222
Young, Malcolm A., "John Booth of Marshfield and Scituate Massachusetts: Servant and Planter," Article in The New England Historical and Genealogical Register - Vol. 159; Pages 220 - 234. Boston, Massachusetts (July 2005): The New England Historic Genealogical Society.
The American Genealogist (v. 74, July 1999
Robert Charles Anderson, Elizabeth Granger, Probable Wife of John Booth of Scituate, Mayflower Descendant, Vol 42, 1992
Jeremy Dupertuis Bangs, The Seventeenth-Century Town Records of Scituate, Mass, 3 volumes
Harvey Hunter Pratt, The Early Planters of Scituate: A History of the Town of Scituate, Mass, 1929
It may be possible to confirm family relationships with John by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with John: