There is a line of HARINGTONs in England with some spectacular ancestry, which has created a great incentive among living HARRINGTONs to connect to them.  Especially desirable is a descent from John HARINGTON & Mary ROGERS, of Somerset, mainly because Mary has royalty in her pedigree.  Most try to connect through their son, James, but other connections are alleged, as well.

Despite all the various connections for them seen in secondary sources, the parents of Robert and Benjamin remain unindentified (see Source 1, below).  There is, however, one thing we do know for certain: Y-DNA testing has proven, beyond any doubt, that Robert and Benjamin are not only not brothers, they are not related in genealogical time.  Robert and Benjamin represent two different origins of surname HARRINGTON.  At best, only one of them, and probably neither, descends from the illustrious HARINGTONs because, and if for no other reason, if they had they would have been well known for that connection in their own time, and they weren't (see Source 2).

And the bottom line is, and as of this writing (30 Dec 2011):  Unless and until we have a proven patrilineal descendant of the Somerset HARINGTONs Y-DNA tested, it is premature for any HARRINGTON of unproven ancestry to be claiming descent from them.  If you are such a HARINGTON, please join the HARRINGTON Y-DNA Surname Project and put this issue to rest.

Robert HARRINGTON, b. 1615/6, England to Watertown, MA
Patrilineal descendants of Robert have a Y-DNA match with a patrilineal descendant of William HARRINGTON of Essex. 

Benjamin HARRINGTON, b. 1618, England to Providence, RI
So far, the descendants of Benjamin have no match "across the pond." 

Abraham ERRINGTON, bap. 19 Jun 1622, England to Cambridge, MA
Abraham is an ERRINGTON, not a HARRINGTON or HERRINGTON, and he is descended from Edward ERRINGTON of Denton, Northumberland.  Abraham's line daughtered out in the second generation.

Rebecca HARRINGTON, b. ca. 1625; d. 4 Dec 1713; m. John WATSON
I have not worked on Rebecca's genealogy.

1.  Patricia Ann Scherzinger.  1996. Colonial Americans of Royal and Noble Descent:  Alleged, Proven, and Disproven.  Heritage Books, Bowie, MD.

p. 248	HARRINGTON   Benjamin (Harrington or Hearnden) - b abt 1624, m Elizabeth White - the immigrant LDS18,71; sufficient proof of alleged royal ancestry is lacking   Daniel - b abt 1748, m Sarah Carpenter - desc/o Benjamin Harrington LDS18   Elizabeth - b abt 1650, m Stephen Northrop - desc/o Benjamin Harrington LDS71   John - b 1651, m Hannah Winter - desc/o Robert Harrington LDS82   John - b 1662, m Lydia Cranston - desc/o Benjamin Harrington LDS18   Jonathan - b 1704, m Sarah Foster - desc/o Benjamin Harrington LDS18
p. 249	HARRINGTON (cont.)   Patience - chr 1697, m David Stowell - desc/o Robert Harrington LDS82   Robert - b 1616, m Susannah George - the immigrant LDS17; royalty not proven   Sarah - b 1671, m Joseph Winship - desc/o Robert Harrington LDS17   Susanna - b 1688, m Joshua Kendall - desc/o Robert Harrington LDS85   Thomas - b. 1665, m Rebecca Bemis - desc/o Robert Harrington LDS85
p. 562	LDS = Michel L. Call, Royal Ancestors of Some LDS Families, 1972

2.  Fredrick Lewis Weis.  1958.  Early Generations of the Family of Robert Harrington of Watertown, Massachusetts, 1634, and Some of His Descendants.  Self-published, Worcester, MA (online at HeritageQuest at Genealogy.com):

p. 9

EARLY NEW ENGLAND HARRINGTON FAMILIES One of the difficulties in dealing with the New England Harrington families is to keep them separate.  There were at least three early Harrington families. I.  Robert Harrington of Watertown, born in England in 1616, who settled in New England in 1634. II.  Abraham Harrington (sic) of Cambridge, whose male descent died out in a generation or two. III.  Benjamin Harrington of Providence, Rhode Island, an entirely different family, possibly though not necessarily, related to the other two...

p. 10

...Genealogists have frequently grouped Robert, Benjamin, and Abraham together as three brothers.  However, there is no least scrap of evidence that such was the case.  It has frequently been said they they were the children of John and Elizabeth (Clinton) Harington, for which there is even less foundation. There were, to be sure, a number of John Haringtons (note the single "r") in England at this period, who were descendants of the ancient Haryngton family.  But had one of these come to New England in the early days, he would at once have been as well known as Dudley, Saltonstall, Winthrop, or Vane, and the other distinguished founders of New England.  No such person appears...