Samuel Gilbert, son of Samuel and Mercy (Warner) Gilbert, was born on 1 May 1712. (alternate source says He was born in Gilead, Conn. on October 16, 1711). Samuel died on 16 Oct. 1774, age 64, at Lyme, Grafton, New Hampshire and was buried on his farm on the bank of the Connecticut River. His wife Abigail died in 1764, aged forty-nine
Elizabeth Curtice on 7 Feb. 1732 at Hebron, Tolland County, Connecticut.The CT marriage record "First Book of Marriages" gives the marriage date for "Gillburd, Samuel Juner Col.& Elizabeth Curtice" as "Feb 7 1732/3"; thus, the correct New Style date would presumably be 07 February 1733. , b. there Jan. 31, 1707-8, d. June 25, 1739, dau. of Samuel and Mary Curtice of Southold, L. I., and Hebron;
Abigail Rowley on May 22, 1740,  b. Hebron, Feb. 13, 1716, d. Oct. 1764, dau. of Samuel and Elizabeth (Fuller) Rowley;
Susannah (Gross) (Morris) Phelps on Jan. 27, 1765, widow of Lieut. Phelps of Hebron and formerly of Dr. Roderick Morris of Hartford. 
Children of this marriage, and their direct descendants, are descendants of Mayflower passengers Edward Fuller and his wife (given name not known) via their younger son, Samuel, who accompanied them in 1620 and survived them -- taken in by his namesake uncle Samuel Fuller, also a Mayflower passenger -- when both parents died during the first winter at Plymouth.
Thomas b. 15 Sep. 1743 married Mercy (Baker) Lathrop.
Annie b 29 Sep. 1745 died 10 April 1748.
John b. 12 Feb. 1749 married Millicent Goodrich.
Abigail b. 31 Jan. 1752 married Rev. Samuel Peters.
Sylvester b. 20 Oct. 1755 married Patience Barber.
Gardiner b. 15 April 1758.
Information about the Gilberts while they lived in Lyme, NH was quite well-documented in a history about Lyme’s early families:
"The HONORABLE COLONEL SAMUEL GILBERT, ESQ." is the inscription upon the slate stone tablet standing at the foot of one grave in the old burying
ground at the river.
The "Turner Genealogy" has "Lydia Gilbert. Her
grandfather, Col. Samuel Gilbert, was one of the first settlers of Lyme NH
and one of the original proprietors of the town.
His son, Col. Thomas
Gilbert, with his wife Lydia Lathrop, and children, removed from Hebron,
Conn., to Lyme in 1773. They had seven daughters and one son, Viz:
Clarissa married Maj. James Cook; Anna, married James Pearson; Abigail,
married John Dimick; Thomas Lathrop married Sally Dimick and widow Deborah
Waite; Lydia, married Jeremiah Bingham; Sally, married Joseph Porter;
Betsey, married Dea. Adolphus Dimick; and Polly, married Ezra Conant, all
of whom reared families and died in Lyme, except Lydia and Polly, who
removed to New York."
The manual of the Congregational church of Lyme has "Samuel Gilbert's
name the 9th on the list of members in the year 1771 and the first on
the list of "deacons and Ruling Elders" 1774, making an apparent error in
one of them regarding the date of immigration.
From his descendants we
have learned that he was born in Gilead, Conn., October 16, 1711, and came
to Lyme from Hebron, Conn., with his son Thomas to assist him in clearing
land and preparing a home for his family; purposing when this was
accomplished to return to his remaining sons in Hebron. It has been
generally supposed that his death occurred about one year after his first
coming to Lyme, but from the dates above quoted, we can but believe that
he lived at least three or four years after. His wife Abigail died in
1764, aged forty-nine.
That he was a man of considerable distinction is
proven by the titles he bore, which were earned in public service. He
was also the possessor of wealth which enabled him to aid his sons
generously in establishing themselves. 
Another (secondary or tertiary) source had birth date as 06 October 1711 and death as 15 October 1774. Sources for those claims are unknown; possible source for 1711 birth date is several death records which estimate his birth in that year. His actual death date is documented on his grave at Gilbert Cemetery. 
(To avoid confusion when researching offspring:) Samuel was indeed the third successive in the line with the same given name; however, he appears repeatedly in the birth records of his children and at least one marriage record as "Jn.R" or "Juner" (Junior), rather than "III", presumably because his grandfather Samuel was by that time out of the picture.
↑ Connecticut Marriages, 1640-1939, database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:F7LW-WWT : 12 May 2016), Samuel, Jn.R Gillburd and Elisibeth Curtice, 07 Feb 1732; citing Hebor, Tolland, Connecticut, United States, Connecticut State Library, Hartford.; FHL microfilm 1,376,165.
↑ Connecticut Marriages, 1640-1939, database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:F7LW-96V : 12 May 2016), Samuell Jr. Gilburt and Abigill Rowley, 22 May 1740; citing Hebor, Tolland, Connecticut, United States, Connecticut State Library, Hartford.; FHL microfilm 1,376,165.
Ancestry.com. Connecticut, U.S., Hale Collection of Cemetery Inscriptions and Newspaper Notices, 1629-1934 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2012.
Thank you to Peggy Shackelford for creating WikiTree profile Gilbert-2952 through the import of Fisher_Shackelford.ged on Dec 11, 2013 and to Gene Gower for creating Gilbert-4119 through the import of BOYLES-GOWER (1).ged on Jan 10, 2015.
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It may be possible to confirm family relationships with Samuel by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: