The further back we trace our families, the more likely it is that we are all related. I recently read several articles of genealogical bent about people trying to prove descent from Charlemagne (apparently the gold standard of ancestors). A common theme of the articles was that each of us is more likely to be descended from Charlemagne than to not be. If you count back the generations each person living today would have in excess of 40,000 great grandparents in Charlemagne's generation. Given the population of Europe at that time, the authors argued that it is likely that most living people have a link to Charlemagne even if they can't prove it.

As to blood ties, my maternal grandfather died as the result of wounds received in WWI (way before I was born). My grandmother eventually remarried (shortly before I was born), and her second husband was the only maternal grandfather I ever knew. Even as a very young child, I knew that we did not have common blood, but to this day, some 30 years after his death I think of him as my grandfather rather than a step-grandfather. I am actively involved in genealogical research of my family, and the man with no blood tie is more meaningful to me than the blood link to several historic ancestors.