Nathaniel + Sarah Vail. Sarah (daughter of Jeremiah Vail and Catherine) was born on 21 Mar 1647 in Salem, Essex Co., MA; died in 1733. [Group Sheet] [Family Chart]

Notes:

http://genforum.genealogy.com/vail/messages/202.html:
"Jeremiah Vail is reputed to be the brother of Thomas Vail who married Sarah Wentworth. As far as I know, and most well versed Vail family researchers will also tell you, is that no conclusive evidence has presented itself to prove this brotherly connection. All the same, it is commonly agreed that this line is the truth. " (Robert Simon Vail III).

http://genforum.genealogy.com/cgi-genforum/pageload.cgi?orange::vail::292. html
I have a Thomas Vail Born 1613 in Southwold,Suffolk, Eng. Died 1687/88 in Westchester, Bronx, NY. Married Sarah Wentworth 1650. Father Jeremiah Vail and Mother Abigail. Son Thomas b. 1662 in of east Chester, Orange, NY. Another son Thomas b.1664 of East Chester, Orange, NY. There is also another, Rev. Thomas Vail of Topeka KS. I will searce that out and get back with you. I have it but not handy right now (Leatha Garner).

Sources and Resources (from Taylor's web page):
Genealogy of the Vail Family Descended from Jeremiah Vail - Henry H. Vail, 1902
Thomas Vail of Salem, Mass 1640 - Wm Penn Vail, 1937
Moses Vail of Huntington, Long Island - Wm Penn Vail, 1947
These genealogies may be found at larger libraries, possibly on LDS microfilm, or can be purchased. See the booksellers at Cyndi's List (try Higginsons and Alton booksellers)
TAG 38:183. - Gives identity of Mary (Folger) Paine Vail.

Other Vail Immigrants (Taylor):
Thomas Vail of Southampton > Westchester - Probable brother to Jeremiah. In 1640 when Thomas Vail with his wife Sarah came to Salem, Massachusetts, Jeremiah Vail was living there, having come in 1639. Jeremiah and Thomas emigrated to the eastern part of Long Island, Jeremiah to Southold, and Thomas to Southampton. Both were blacksmiths by trade.

George Vail did not exist! - there was no George Vail of Huntington, Long Island, as reported by an early Vail genealogy. Moses Vail, of that old genealogy, is son of Joseph, son of immigrant Thomas (who was probably brother to immigrant Jeremiah.) George Vail never existed and is a complete fabrication. See "Genealogy of Moses Vail of Huntington, L.I.: Showing his Descent from Joseph Vail, son of Thomas Vail of Salem, Massachusetts", 1640, by William Penn Vail, 1947. (Contributed by Oronoco98@aol.com)

James Vail - reported by Savage in New England Dictionary: "James Vail: Dedham, by w. Ann had James, bapt. 6 July 1656; John, 17 Oct. 1658". His relationship to Jeremiah of Long Island, if any, is unknown to me.

Will of Jeremiah Vail. I have seen reports of a will for Jeremiah Vail (Made: 12/04/1685, Probated: 10/19/1687, Southold, NY). I have been all through the New York Wills book and can't find it. Where is it?

Need more evidence: I would appreciate any more evidence that anyone can contribute that the wife of Nathaniel Moore (Sarah) was the daughter of Jeremiah Vail. I have found this link in several secondary sources, but do not know the evidence on which it is based (ie naming of Nathaniel Moore in Jeremiah's will, marriage record, etc.)

Jeremiah + Catherine. was born about 1618 in England; died between 1649 and 1660. [Group Sheet] [Family Chart]