To my mind there are three ways to be related to a president. You can share medieval ancestors with them; you can share colonial ancestors with them; or you can be a closer relation than that. I mean someone is Barack Obama's second cousin. One of the purposes behind Ancestors of American Presidents (AAP) by Gary Boyd Roberts is to discover how you are related to a given president.
Would it surprise you to find out that 25 of the 43 men to be president was of royal descent? That's a staggering 58% of presidents. This goes to show you that up to 2008 we were drawing on a very insular group of people from within our country for two hundred years. Let's face it one black person out of 43. One Catholic out of 43. That's a lot of straight, white, protestant men to talk about.
So, off the bat if you have a valid royal line, you can be related to at least 25 of the men who were presidents. That involves sharing some medieval ancestor and being 20-30th cousins with the president.
The presidents who are royally-descended are:
John Quincy Adams
William Henry Harrison
Abraham Lincoln (a very problematic descent. Nothing is known of his mother Nancy Hanks, so her entire ancestry is complete conjecture)
Rutherford B. Hayes
William Howard Taft
Warren G. Harding
Franklin D. Roosevelt
Harry S Truman
James E. Carter
George H.W. Bush
George Walker Bush