Interesting thread and the replies express a truth many of us need to be reminded about.
Getting back to your original topic, cebconsulting -
the answer is ALL maternal-paternal lines share ancestors.
Read about the phenomenon of PEDIGREE COLLAPSE here,
Everybody has to have the same set of ancestors (same couple) on more than one family line, at many points in their family history. Your pedigree should reach a maximum "girth" and then dwindle - it is a diamond shape, not a fan.
The general rule of thumb (which would vary from individual to individual) is that the number of grandparents doubles every 25 years. Go back 1200+ years to 800 AD using this guideline, and you should have 281.5 trillion grandparents - but there weren't that many people on the planet at that time.
Take a look at this chart "How Many Ancestors Do You Have" to check out the situation in the 13th and 14th generation: http://familyforest.com/resources/51/ancestors-at-a-glance
At 13 generations back, you theoretically have 8,192 ancestors. At 14 generations, that doubles to a theoretical 16,384 ancestors. The number of ACTUAL individuals who are your ancestors will depend on where and how your ancestors lived, as was already pointed out. One chunk of mine were peasant farmers in Europe (true for most of us), bound by law to stay in the area where they lived. This broad band of the lowest social class did not travel much. Of course people married 2nd and 3rd and 4th cousins, creating pedigree collapse. Same was true at the top of the social ladder, and I have some of that too. European royals have far fewer actual ancestors than the math would suggest, because cousins married.
At the simplest level, consider a brother and sister marrying. Their child would have two actual grandparents instead of a theoretical four. That's pedigree collapse.
There's a lot written on this topic - I didn't search for the most authoritative sources, just posted the first "hits" I got on Google. :D