Some believe John's wife is Jane STRONG, but there is no proof of the connection [see Comments below].
Wife:  Jane STRONG
Birth:  ca. 20 Mar 1609/10, Chardstock, Dorset, ENG
Father:  Thomas STRONG
Mother:  Joanna BAGGE

1.  Timothy Hopkins.  1932.   John Hopkins of Cambridge, Massachusetts, 1634, and Some of His Descendants.  Stanford Univ. Press, Stanford, CA.   John Hopkins's wife is given only as "Jane."

2.  Timothy Hopkins.  1948.  "Stephen Hopkins of the Mayflower* and Some of His Descendants." New England Historical and Genealogical Register 102(1): 46-60.  On p. 46 is an editorial footnote to the title of the article:

*I have no reason to believe that John Hopkins of Hartford was related to Stephen of the Mayflower.  I have seen statements that he was the son of Stephen; but as Stephen does not mention him in his will and Bradford makes no reference to such a son of Stephen and no one has found any authority which is based upon any fact, I do not think that any faith can be placed in such statements.  (Letter of T.H., 28 April 1908.)

3.  John Farmer.  1829.  Genealogical Register of the First Settlers of New England.  Carter, Andrews & Co., Lancaster, MA (republ. 1964/69 by Genealogical Publ. Co., Baltimore; online at GenealogyLibrary.com).   On p. 149:

JOHN, Cambridge, was admitted freeman 1635.

4.  The Will of John Hopkins names wife, Jane, and two underage children:  Stephen and Bethiah. 

5.  Clarence Almon Torrey.  1997.  New England Marriages Prior to 1700.  Genealogical Publ. Co., Baltimore.  On p. 387:

HOPKINS, John (-1654) & Jane __?__, m/2 Nathaniel WARD, m/3 Gregory WOLTERTON; b 1634; Cambridge / Hartford, CT.

The "b 1634" is supposed to indicate the birth date of a child as an indication that the marriage took place before this time.  I say "supposed to" because I know of no birth record for Stephen, 1634 or otherwise (see comments below).   The locations given by Torrey are known residences of the husband, ending with the husband's place of death.  An entry in Torrey does not imply a marriage in New England; it only demonstrates the presence of a married couple there before 1700.  Torrey is not a compilation of primary records; it is a compilation of secondary published sources.

6.  Gary Boyd Roberts.  1995.  Ancestors of American Presidents.  New England Historic Genealogical Society, Boston, p. 27.  John Hopkins's wife is given only as "Jane ----."

7.  LDS.  Family Search: Internet Genealogy Service:  AF - Ancestral File (online at FamilySearch.org):  names "Jane STRONG" as the wife of John HOPKINS.

8.  See the Ancestry of Elder John Stronge at Martha Strong's web site [link died].

9.  Archives of the STRONG-L mailing list (online at RootsWeb.com):  in posts to the list, Martha Strong is adamant that Jane STRONG was not the wife of John HOPKINS.

A.  The identity of John Hopkins's wife as Jane Strong, daughter of Thomas & Joanna (Bagge) Strong, is controversial, and I have yet to find any hard evidence proving Mrs. Jane Hopkins is Jane Strong of Chardstock.   The reason for its importance is that Jane Strong's grandfather, George Strong, has some illustrious descendants.  The temptation to make the connection, despite lack of a firm connection, is very strong.   On the other hand, there is no evidence disproving it, either.  That is, the fate of Jane Strong of Chardstock in England appears to be unknown.  Her parents died in England, so she could not have come to America with them.  Social taboo would have prevented a single woman from making the journey on her own, so many have assumed she and John were married in England.   That no record of their marriage has been found in New England supports that theory, though many marriage records have, of course, been lost.  There is another possibility.  Jane Strong's first cousin, John Stronge (a.k.a., "Elder John Stronge"), came to Hartford in 1635 on the Hopewell "with his family," which could have included Jane.  An arrival of Jane Strong in Hartford in 1635 puts her in a position to meet and marry John Hopkins when he moved to Hartford in 1636.  However, these circumstances only mean that it is possible that John's wife was Jane Strong.  But we now have a Stephen born in 1637, which would make him four years younger than his wife, Dorcas.  Not impossible, but unlikely.

B.  Stephen Hopkins was born, with absolute certainty, after 1 Jan 1626/7 and before 1 Jan 1648/9.  Stephen's wife, Dorcas, was baptized in late 1633 and was probably born earlier in the year.  The average married man is four years older than his wife, so a birthyear ca. 1629 would be reasonable for Stephen, except that his father, b. 1613, would have been too young at the time.   The ca. 1634 date of Torry is, thus, not unreasonable.