All of Henry VIII’s six wives were related to each other–and to Henry–by a common ancestor, King Edward I (“Longshanks”). Henry was Edward’s seven- and nine-times great-grandson on his mother’s side and his six-times great-grandson on his father’s, while all of his wives–including the Spanish-born Katherine of Aragon and the German-born Anne of Cleves–were Edward’s seven-, eight-, or nine-times great-granddaughters.*
To the best of my ability, here are the wives’ ancestry dating back to Edward I.
Edward I → Edward II → Edward III → John of Gaunt → Philippa of Lancaster → Infante John of Portugal → Isabel of Portugal → Isabel of Castile → Katherine of Aragon
Edward I → Thomas of Brotherton → Margaret, Duchess of Norfolk → Elizabeth de Segrave → Thomas Mowbray → Margaret Mowbray → John Howard → Thomas Howard → Elizabeth Howard → Anne Boleyn
Edward I → Edward II → Edward III → Lionel, Duke of Clarence → Phillippa of Clarence → Elizabeth Mortimer → Elizabeth Percy → Mary Clifford → Henry Wentworth → Margaret Wentwoth → Jane Seymour
Edward I → Margaret, Duchess of Brabant → John III of Brabant → Margaret of Brabant → Margaret III of Flanders → John I of Burgundy → Marie of Burgundy → John I, Duke of Cleves → John II, Duke of Cleves → John III, Duke of Cleves → Anne of Cleves
Edward I → Thomas of Brotherton → Margaret, Duchess of Norfolk → Elizabeth de Segrave → Thomas Mowbray → Margaret Mowbray → John Howard → Thomas Howard → Edmund Howard → Kathryn Howard
Edward I → Edward II → Edward III → John of Gaunt → Joan Beaufort → Richard Neville → Alice Neville → Elizabeth FitzHugh → Thomas Parr → Katherine Parr
While Anne Boleyn and Kathryn Howard were famously the most closely related of Henry’s wives as first cousins, (Anne’s mother was a sister of Kathryn’s father), Katherine of Aragon, Jane Seymour, and Katherine Parr all share a closer common ancestor in Edward III, and the first and last of Henry’s Katherines were both descended from John of Gaunt, who was Aragon’s three- and Parr’s four-times great-grandfather, respectively.
It’s also possible that some or all of these women were descended from other members of the English royal family in yet more ways, but these are the lines that I was able to follow. Until very recently I had no idea that all of Henry’s wives, even Anne of Cleves, were related to him; I thought it was kind of wild!
* This may not be the precisely correct terminology, as I’m no genealogist.