William Shakespeare and Anne Hathaway had three children.
The eldest, Susanna, was baptized on May 26, 1583, and married John Hall in 1607. They had one child, Elizabeth, in 1608. Elizabeth was married twice, to Thomas Nash in 1626, and to John Bernard in 1649. However, she had no children by either husband.
William and Anne also had twins, Judith and Hamnet, who were baptized on February 2, 1585. Hamnet died at age 11 and a half.
Judith married Thomas Quiney in 1616, and the couple had three sons: Shakespeare Quiney, who died in infancy, and Richard and Thomas, who both died in 1639 within a month of each other. Since neither of the boys married, there is no possibility of any legitimate descendants from Shakespeare’s line.
It is possible, however, to claim a relationship to Shakespeare through his sister, Joan. She married William Hart some time before 1600 and there are many descendants of this marriage alive today, in both the male and female lines.