At which point in time are we related to everyone?

Okay, I remember this from history cl a few years ago. The theory is that, technically speaking, everybody is related and few people are more than seventh cousins from one another. Part of the theory was also that the further one goes back in time, the higher liklihood that anyone living during that time is your ancestor (so probably everybody in the world (or at least all Europeans) could say they're related to Julius Caesar). Is this true? If so, at which point (year) is it that we share most of our ancestors. If I were to say I was related to a specific person living in 1200 A.D., what's the chance that anybody I meet on the street also has this person as an ancestor?