Charles and Diana: 7th cousins, 1x removed
Prince Charles and his first wife, born Lady Diana Spencer who eventually was styled as Diana Princess of Wales, were seventh cousins once removed via William Cavendish, 3rd Duke of Devonshire.
The Duke and Duchess of Cambridge: 11th cousins 1x removed
Although Catherine Middleton is considered a commoner (in that she isn’t a peer of the Queen based Britain’s peerage system), she is actually related to her husband, Prince William, albeit distantly. They are 11th cousins once removed, via Sir William Blakiston, a Baronet (whose peerage Catherine was not eligible to inherit).