There have been many studies using yDNA analysis to answer historical questions. Here are a three of the most famous.
Dr. Bryan Sykes, a geneticist at Oxford University tested men all over England who have the surname Sykes and variants. Genealogists had theorized that the surname Sykes was used by dozens of unrelated families. However, the study showed that about 50% of the Sykes men tested had the same y chromosome. Assuming an infidelity and adoption rate of about 2% or 3% per generation since the Middle Ages, this is about the percentage of modern Sykes men who should have the Sykes y chromosome if there is only one Sykes family. So, instead of showing that there are dozens of different Sykes families in England, the study seems to show that there is only one Sykes family — but not everyone who belongs to the family is biologically descended in the male line from the first Sykes.
The descendants of Sally Hemings have an old tradition that Thomas Jefferson was the father of her children. In 1998 Eugene Foster undertook to test the tradition using yDNA analysis. He compared samples from male-line descendants of Sally Hemings’ son Eston Hemings with samples from male-line descendants of Thomas Jefferson’s uncle Field Jefferson. The test results proved that Eston Hemings’ father was a Jefferson, but the test cannot show whether Eston’s father was Thomas Jefferson himself. Most historians now accept that Thomas Jefferson was the father of Eston Hemings, and that Jefferson was probably the father of all six of Sally Hemings’ children. The Jefferson family belongs to Haplogroup T* (fomerly K2). See Wikipedia, Jefferson DNA Data.
Michael Hammer, a geneticist at the University of Arizona tested a large number of Jewish men who have the surname Cohen or who have a family tradition that they are cohanim. Jews believe that the surname Cohen indicates that a man is a cohen (priest), descended in the male line from Aaron, the brother of Moses. A high percentage of the test subjects share the same y chromosome and apparently have a common origin in the Middle East. Researchers suggest that these men descend in the male line from the Biblical Aaron, confirming tradition. Critics point out that a single prolific Rabbi living 1,000 years ago could account for the matches. The Cohen lineage belongs to Haplogroup J2. See Wikipedia, Y-Chromosomal Aaron.