Note that a mere mistake in paper genealogy uncovered by DNA testing is, strictly speaking, not an NPE.  It's just bad genealogy, a genealogy that can be corrected by finding additional evidence or re-interpreting the existing evidence.  The event becomes an NPE when the paper genealogy is seemingly correct, but is contradicted by DNA test results.

Keep in mind that before the late 20th Century, adoptions were usually kept secret, frequently because the child was born of an unwed mother and being a bastard child carried a severe social stigma.  It was also generally believed to be psychologically damaging for the child to be aware that he or she was adopted, so a child was apt to never be told they had been adopted.  As for extra-marital relationships, not much has changed with regard to the desire of the wandering spouse to keep the relationship secret.  What is different is that, in the past, the family's fear of scandal was likely to lead to the affair being hushed up and the marriage remaining intact, at least superficially, while today an affair can more easily lead to divorce.  The bottom line is that cultural conditions in the past were conducive to generating NPEs.

While it may seem that an NPE is a genealogical disaster, with the aid of DNA testing it is possible to unravel them to one degree or another.  To illustrate what is possible, given below are brief descriptions of the NPEs revealed in the Y-DNA surname projects I administer, including the degree to which they've been resolved.

Ira CORBIN was born in Massacusetts and died in South Carolina.  With Ira being from Massachusetts, it was expected his descendant would be a DNA match to tested descendants of Clement CORBIN, the major progenitor of CORBIN in New England.  Results revealed there was no possibility of a connection because Clement's descendants are Haplogroup G2a and Ira's descendant is Haplogroup R1b.

Ira's descendant is, however, a tight genetic match with a well-known New England SHERMAN family.  There are, in fact, several marriages in New England and New York between these SHERMANs and the descendants of Clement CORBIN, so Ira's paper ancestor will probably turn out to be one of them.

Until we have enough cousins of this individual tested, we won't know where in his lineage the NPE took place, but there does seem little doubt that it occurred in New England, where these two families were interacting, because these SHERMANs are notably absent from SC.

Wilmer ROBISON was the child of Rebecca A. STEPHENS, daughter of Joshua STEPHENS & Caroline CORBIN.  Wilmer was born out of wedlock, before Rebecca's marriage to Benjamin Harrison ROBISON, who later adopted Wilmer and gave him his name.  Family legend was that Wilmer was the product of a relationship between Rebecca and her first cousin, Elmer Ellsworth CORBIN, a descendant of the Clement CORBIN mentioned above.  Testing of a descendant of Wilmer revealed that he could not be a descendant of Clement because, as above, he is Haplogroup R1b, not G2a.  His results did reveal, however, that he is genetically a STEPHENS.

It appears that Rebecca didn't have an affair with one of her CORBIN cousins, but one of her STEPHENS cousins — or the darker interpretation that she was abused by one of her STEPHENS relatives.  Rebecca was an adult when Wilmer was conceived, so the latter seems unlikely.  So, as it turns out, instead of having a double dose of CORBIN genes, this individual has a double dose of STEPHENS genes. 

Because all of Rebecca's near STEPHENS kin will likely have the exact same Y-DNA test results, it's unlikely that Wilmer's actual father will be identified, unless court records can be found of a bastardy claim or assignment of a guardian.  This testing did accomplish something else, though. 

Prior to this test, they did not know which STEPHENS family they were part of, making this the first time in my experience that Y-DNA testing of a son identified the patrilineal origin of the mother!

Jacob STROUP II is, on paper, a son of Adam, son of Jacob STROUP I, son of Johann Pieter STRAUB, the 1733 immigrant to Philadelphia, PA.  The problem is that the three tested descendants of Jacob II (each through a different son) are Haplogroup J2, so are not a match with the descendants of his alleged brothers and all the other descendants of Johann Pieter STRAUB, who are all Haplogroup I1. 

These descendants of Jacob II are, however, a close DNA match with a BIDDLE.  I have been unable to obtain this BIDDLE's lineage, and I have yet to find where these families crossed paths, but it does appear likely that our STROUP is really a BIDDLE.

The paper connection from Jacob II to Adam does seem sound (on a deed, Jacob names his father as Adam).  As Jacob II is Adam's eldest child, the most likely explanation is that Jacob was a child from a prior marriage of Adam's wife, Catherine.  Unfortunately, the lack of early marriage records in NC greatly hampers the resolution of this NPE.

It is not yet known where in the patrilineal line of descent from Silas BELEW to the test subject the NPE occurred, but we know one did occur because the testee is genetically a STROUP.  Examining the evidence, we find that in the 1850 census, Silas BELEW was listed next to Harmon STROUP, a member of this particular STROUP family.  We also continue to find relationships between these STROUPs and BELEWs for the following censuses up through 1930.  Further testing of cousins could pinpoint the generation in which the NPE occurred, and deeper research in county court records might produce guardianship records or a bastardy claim that could resolve this NPE entirely.

Even before a patrilineal descendant of Jacob Jackson STROUP was DNA tested, I had suspected he was adopted because he and a sister, Mary, appeared late in the marriage of their parents, Jacob & Mary (KETTERING) STROUP.  This suspicion was supported when Jacob's patrilineal descendant turned out not to be a DNA match with these STROUPs, but instead, to be a tight genetic match with a German NEUHAUS / NEWHOUSE family.

An examination of county records revealed a deed showing the STROUP and NEWHOUSE families owned adjacent land in Wythe County.  Evidence further shows that the only NEWHOUSE living in the area at the time Jacob was conceived was John NEWHOUSE, and that John's first wife died about the time Jacob was born or within a year or two afterwards.  John NEWHOUSE then left the state and remarried, with no children from his prior marriage evident in his new household.

There seem to be two most likely possibilities:  1) that the childless STROUP couple adopted John's child (or children if Mary is, indeed, Jacob Jackson's sister) after John's first wife died, or 2) that John NEWHOUSE had an affair with Mary (KETTERING) STROUP, which would also mean the couple's infertility was caused by Jacob, not Mary.  If there was a legal adoption and if county records are extant, it may be possible to find a record of the adoption or the assignment of a legal guardian.

This individual descends from William Waitsel CRUMP, son of unwed mother, Rebecca CRUMP, who sued Waightstill PRESTWOOD for bastardy over the birth of William in 1878 in Caldwell Co., NC.  We would have expected William's patrilineal descendant to possess a PRESTWOOD Y-chromosome, but it turns out he is a 66/67 match with the STROUPs of Gaston Co., NC.  It appears the NPE must have occurred later, after William left Caldwell County (where there were no STROUPs) and settled in Gaston County (where there was an abundance of STROUPs), but it will take some testing of cousins to pinpoint the individual who bears the STROUP Y-chromosome for the first time.  Update:  his father has now been tested, and he is a match (i.e., is also a STROUP).

Five paper descendants of Peter CORBIN of Pickins Co., SC, are a close match with each other, but a sixth is not, so apparently he has an NPE in his lineage.  As yet, he has no close DNA match, so we have not determined his "true" surname.

Even though a paper connection has never been made, based on his migration path, Charles CARRICO of Maryland, Washington Co., KY, and Sullivan Co., IN, has always been assumed to descend from Peter CARRICO, 1674 immigrant to Maryland.  DNA testing of descendants through his sons Josiah and Basil now supports that Charles is, indeed, descended from Peter I.  However, testing of two brothers descended through Charles's paper son, Reason CARRICO, are not a match to the other descendants of Charles.  One of these brothers has been tested to 67 markers, and he does have a near match (GD of 4) with a LITTLETON.  The only obvious place where the two families appear to have crossed paths pre-20th Century would be in Maryland or Kentucky, so the NPE would most likely have been early in his lineage.  This NPE may, in fact, resolve a long-standing issue that Reason's birth (8 Feb 1794) is too closely spaced with his brother Basil's birth (11 May 1794), so it may be that what we have uncovered is support for Reason having been adopted, while putting to rest the issue of the births being too closely spaced.

Lawson Sidney STROUP was born out of wedlock to Elizabeth STROUP, a member of the well-known and prolific STROUP family of Gaston County, North Carolina.  Not surprisingly, a patrilineal descendant of Lawson is not a Y-DNA match with these STROUPs.  We do find that he has a match with three surnames:  two 12/12 matches with SELLERS, one 25/25 match with a QUEEN, and one 36/37 match with a COPE.  Their haplotype is rare (unique just to them), and it appears (for reasons given on the page linked above) that all five are actually SELLERS.

An examination of the 1880 census shows a young, unmarried Elizabeth STROUP living with her parents in Gaston Co., NC, surrounded by SELLERS households.  These SELLERS are all descended of a well-known German SÖLLERS / SOELLERS / SELLERS progenitor, with which our subject is a DNA match.  Unless there is an extant bastardy claim by Elizabeth in the county court, it is unlikely the actual father of Lawson will be identified, but there is no doubt where his patrilineal ancestry lies.

I urge the QUEEN and the two SELLERS to upgrade to 37 markers to solidify the match, though their haplotype is sufficiently rare that I don't doubt all five have a near common ancestor.  Their common ground appears to be North Carolina, and when I have time to extract their census records (ha!), I'll be looking to see exactly where the COPE and QUEEN lines crossed paths with the SELLERS.