Doug Rohde's paper on the most recent common ancestor of all humanity is the most interesting of the numerous pieces of research cited by Mark Humphrys on this topic. Rohde set up a computer simulation of global population dynamics from 20,000 BC to the present day, including a fairly small allowance for migration rates between continents.
He found that his computer simulations gave results of between 3,000 and 5,000 years ago for the lifetime of the most recent common ancestor of all humanity. Reading through his paper, it seems clear to me that his conclusions are too modest; that in fact it is entirely likely that the most recent ancestor of all humanity lived around 2,000 years ago. I have several reasons for thinking this:
1) Rohde admits that he is using unrealistically low rates of inter-country migration, simply so as not to get results that are too startling. If the real rate of migration between countries and continents is higher than the one he used, the time to the most recent common ancestor decreases.
2) His models assumes that women have an equal probability of bearing children every year between the ages of 16 and 40, thus giving an average age difference between mothers and their children of 28. I reckon this flattens out the natural bump (!) at the lower end of that age range, and my suspicion (without any proof) for most of human history is that most children were born to women aged between 14 and 30. That too will decrease the time to our most recent common ancestor, as the time between generations will be shorter.
(A digression: female-female lines are much harder to trace, which is odd given that there is never any doubt about who a child's mother is. For instance, little is known of Mary Garritt, the wife of Thomas Webb, a surveyor in Stow-on-the-Wold in the mid-18th century. Her daughter Frances (1775-1862) married Thomas Salisbury, landlord of Marshfield House in Yorkshire. Their daughter Anne (1806-1881) married another gentry type, Edwyn Burnaby of Baggrave Hall in Leicestershire. Their daughter Caroline (1832-1918) married a widowed clergyman who was the grandson of a duke. Their daughter Nina (1862-1938) managed to bag an earl as her husband. Her daughter Elizabeth (1900-2002) did rather better than a mere earl. Her daughter, another Elizabeth, was born in 1926 and is still alive; those of you in the UK and Canada will find her depicted on certain useful everyday objects, ie money. But her direct female line ancestry can be traced back only six generations before it is lost in the Gloucestershire middle classes.)
3) Rohde leaves out the effect of occasional exceptional individuals (what in homage to Asimov we might call the "Mule effect"), in this case those with vast numbers of children all of whom produce descendants, such as Genghis Khan. The paper I link to there shows that Genghis Khan's Y-chromosomes are present in large proportions of the male population of his former empire.
That of course only measures the direct male-line descent of the individuals concerned. It must be pretty certain that if you take all lineages into account, Genghis Khan is an ancestor, quite likely the most recent common ancestor himself, of everyone between the Aral Sea and the Pacific north of the old boundary line. If he had not fathered the immense number of children he appears to have done, that would surely have added another couple of centuries to the time since the most recent common ancestor of the people of the region.
I've argued elsewhere that most of us are descended from the Prophet Muhammad. Someone living in the first few centuries AD, probably in East Asia, probably a man with children by several different women (quite possibly in different places), is the most recent person who is the ancestor of us all.
Of course, while this is a nice concept, it's not quite as strong as it seems. Rohde points out one reason for this, which is that at the distance of 50 generations the likelihood that we have inherited any genetic material at all from this one particular ancestor is pretty minimal unless you happen to be fairly close in geographical proximity to them.
There is another reason as well, which is that family ties are not just about genetics but are also about how you feel. By emphasising the arrival of children in a family as the product of procreation between married couples of opposite sexes, the Most Recent Common Ancestry model leaves out all the messiness of real life - adoptions, most obviously, but various other possibilities are all around us. It's an attractive mathematical concept, but we have to bear in mind that it isn't the whole story.