Rem Jansen was probably born before 1620.

He married Jannetje Jorise Rapalje, daughter of Joris Janszen Rapalje and Catalyna Trico, at Reformed Dutch Church, New Amsterdam, on 21 December 1642 "Remmet Janszen, j.m. Van Jeveren, en Janneken Rapalje, j.d. Van N. Nederlt"
Samuel S. Purple, Records of the Reformed Dutch Church in New Amsterdam and New York; Marriages from 11 December 1639 to 26 August 1801 (Bowie, MD: Heritage Books, reprint 2003, original 1890 NYG&BS), p.12.

Witnessed the baptism of Jeronimus Joriszen Rapalje , son of Joris Janszen Rapalje and Catalyna Trico, on 28 June 1643 at Reformed Dutch Church, New Amsterdam, (sponsors Hans Hanszen, Rem Janszen, Jannetje Rappalje).
"Records of the Reformed Dutch Church in New York", New York Genealogical and Biographical Record Vols.5- (1874-): 5:33. Jeronymus; parents: Joris Rappalje; witnesses: Hans Hanszen, Rem Janszen, Jannetje Rappalje.

Witnessed the baptism of Kniertie Hendricks , daughter of Hendrick Willemszen and Femmetie Joosten, on 24 October 1649 at Reformed Dutch Church, New Amsterdam, (sponsors Rem Janszen, Claertje Abels, Annetje Daniels).
Ibid., 5:93.

Rem (Remmer) Jansz, from Jewerden (Jeveren, or Jever, in Oldenburg), smith, was at New Amsterdam as early as 1638, and in 1643 owned land on Long Island. Early in May 1650, he obtained from the authorities of Rensselaerwijck a lease of a garden adjoining the churchyard, and is referred to as being an Inwoonder in Fort Orangien (inhabitant of Fort Orange).
A.J.F. van Laer, Settlers of Rensselaerswyck 1630-1658 (Baltimore: Genealogical Publishing Co., 1965, 1980), page 41.

Witnessed the baptism of Jacomyntie Pieterse Van Nest , daughter of Pieter Pieterszen van Nest and Judith Jorise Rapalje, on 29 May 1661 at Reformed Dutch Church, New Amsterdam, (sponsors Rem Janszen, Jan Joriszen, sara Montfoort).
"Records of the Reformed Dutch Church in New York", New York Genealogical and Biographical Record Vols.5- (1874-): 6:93. Jacomyntie ; parents: Pieter Pieterszen, Judith Joris.

Witnessed the baptism of Aeltje Teunise Bogaert , daughter of Teunis Gysberts Bogaert and Sarah Jorise Rapalje, on 13 November 1661 at Old First Dutch Reformed Church, Breuckelen (Brooklyn), Kings Co., Long Island, New York, (sponsors Rem Jansen, Maria Fredericks).
Baptisms in the Reformed Dutch Church of Brooklyn as per the records of said Church from Oct. 31, 1660 to Dec 13, 1719: From Corporation Manual of the City of Brooklyn, 1869, pages 448 to 504; FHL film #0017529, item 4 (Salt Lake City: Filmed by the Genealogical Society of Utah, 1939), Copied and translated from the Dutch by Teunis G. Bergen. Filmed from the typed manuscript in the Holland Society of New York, p.449.
A. P. G. Jos van der Linde, Old First Dutch Reformed Church of Brooklyn, New York: First Book of Records, 1660-1752, New York Historical Manuscripts: Dutch (Baltimore: Genealogical Publishing Co., Inc., 1983), page 110. Aeltie; parents Teunis Gijsbertse, Sara Joris, "from the Walebocht".

Witnessed the baptism of Geertie Dorland , daughter of Jan Gerritszen Dorland and Annetje Remse, on 19 August 1674 at Old First Dutch Reformed Church, Breuckelen (Brooklyn), Kings Co., Long Island, New York, (sponsors Rem Janssen, Hillen Remsen).
Ibid., page 116. Geertje; parents: Jan Geritsen Dorlant, Anna Remsen, from Breukelen.

Rem Jansen and Jannetje Jorise Rapalje were members of the at Reformed Protestant Dutch Church, Flatbush, Kings Co., Long Island, New York, in 1677 from the Wallabout.
David William Voorhees, editor, Records of The Reformed Protestant Dutch Church of Flatbush, Kings County, New York, Vol.1, 1677-1720 (New York: Holland Society of New York, 1998), page 353. Old Members found here in the 4 Villages in the year 1677. From the Wallabout. Died Feb 1681 Rem Jansz and wife Jannetje Joris Rapailie.

Witnessed the baptism of Jannetje Hegeman , daughter of Joseph Adriaenszen Hegeman and Femmetje Remse, on 20 October 1678 at Reformed Protestant Dutch Church, Flatbush, Kings Co., Long Island, New York, (witnesses Jannetje Joris Rapailie, Rem Jansz).
George E. McCracken, "Catalyntje Trico Rapalje", The American Genealogist vol.35 (1959): 35:199.
David William Voorhees, editor, Records of The Reformed Protestant Dutch Church of Flatbush, Kings County, New York, Vol.1, 1677-1720 (New York: Holland Society of New York, 1998), page 388. Jannetje; parents: Joseph Hegeman, femmetje Rems; op Midwoud.

Rem Jansen and Jannetje Jorise Rapalje were members of the at Reformed Protestant Dutch Church, Flatbush, Kings Co., Long Island, New York, on 19 November 1679 "in the Wallabout."
Ibid., page 333 Register of the Members from the Four Villages. 19 Nov 1679. In the Wallabout. Rem Jansz (Died Feb 1681) and wife Jannetje Joris Rapailie (note says, "left for N. York with certificate).

Children by Jannetje Jorise Rapalje b. 18 Aug 1629:
Annetje Remse b. 12 Mar 1645
Belitie Remse b. 20 Jan 1647
Jan Remsen b. 12 Jan 1648, d. before 15 Aug 1697
Joris Remsen b. 2 Feb 1650
Rem Remsen b. 2 Dec 1652
Hillitje Remse b. 16 Sep 1653
Catalina Remse b. 4 Oct 1655
Femmetje Remse b. 1 Aug 1657
Jannetje Remsen b. bt 1658 - 1662
Jacob Remsen b. 19 Mar 1662
Jeronimus Remsen b. 1664, d. between 1 Oct 1746 and 8 Oct 1750
Daniel Remsen b. 1665
Abraham Remsen b. 16 Sep 1667
Sarah Remse b. 6 Dec 1670
Isaac Remsen b. 16 Sep 1673
Jeremias Remsen b. 10 Sep 1675, d. 3 Jul 1757
George E. McCracken, "Catalyntje Trico Rapalje", The American Genealogist vol.35 (1959): 35:196-7.
Patricia Law Hatcher, Henry B. Hoff and Robert W. Hull, "Reymerigh - An Unusual Given Name Ties Together the Norstrand Family", New York Genealogical and Biographical Record Vol.139, page 32 (Jan 2008): 139:36.
Baptisms in the Reformed Dutch Church of Brooklyn as per the records of said Church from Oct. 31, 1660 to Dec 13, 1719: From Corporation Manual of the City of Brooklyn, 1869, pages 448 to 504; FHL film #0017529, item 4 (Salt Lake City: Filmed by the Genealogical Society of Utah, 1939), Copied and translated from the Dutch by Teunis G. Bergen. Filmed from the typed manuscript in the Holland Society of New York, p.450.

Rem Jansen died in February 1681.
David William Voorhees, editor, Records of The Reformed Protestant Dutch Church of Flatbush, Kings County, New York, Vol.1, 1677-1720 (New York: Holland Society of New York, 1998), page 333 Register of the Members from the Four Villages. 19 Nov 1679. In the Wallabout. Rem Jansz (Died Feb 1681) and wife Jannetje Joris Rapailie (note says, "left for N. York with certificate).

Bio includes data from The Brouwer Genealogy Database.
http://freepages.genealogy.rootsweb.ancestry.com/~brouwergenealogydata/surname_index.htm (findagrave.com)