The most recent common ancestor (MRCA) of all Europeans lived as recently as 600 years ago. And a 2013 study showed that if you go back 1000 years, you would find that all Europeans are indeed descended from the same set of ancestors. Think about it: Not only one common ancestor, but the same set of ancestors. What this means is that if a person living at that time (c. 1000 CE) has any descendants living today, everyone in Europe is descended from that person. This is the reasoning behind the argument that every European is a descendant of Charlemagne (742-814), and I am prepared to accept it.
Similar arguments can be (and probably have been) made for other parts of the world; I am only using Europe as an example. A 2004 study argued that the most recent common ancestor of all humans lived around 1500 BCE in eastern Asia. This means that if you could trace your full ancestral tree back to 1500 BCE, this person from eastern Asia would figure in your ancestral tree at least once. The rest of your ancestors could be completely different people (although this is unlikely, since your total number of possible ancestors in 1500 BCE would exceed the total population of the world at the time, necessitating a significant amount of pedigree collapse).
The same 2004 study also argued that "in 5,400 BC, everyone alive was either an ancestor of all of humanity, or of nobody alive today". This is the identical ancestors point of the human population.
So, does this mean that there is no point in doing genealogy? After all, we know for a fact that we're all related anyway!
First of all, a thousand years is a very long time in historical and genealogical terms. Although every European may well be descended from the same ancestors in 1000 CE, that still gives a full millenium of families branching, re-intertwining, moving around, loving and warring and living their lives. A thousand years means a lot of ancestors to explore - not to mention siblings, cousins, and so on. A thousand years should be more than enough for anyone to do their genealogical explorations. Another point that needs to be made is that nobody - yes, nobody, not even the Queen of England or the Emperor of Japan - will ever be able to trace every single one of their ancestral lines back to 1000 CE, simply because there are not enough records. It is not only unlikely, but literally impossible. Even if all sources are exhausted, there will still be mysteries and holes left in your pedigree, no matter who you are.
Most people (or most Norwegians, at any rate) rarely manage to dig back further than about 500 years anyway, and even if they do have a few noble or royal lines going back further than that, those lines will likely comprise only a tiny percentage of their total ancestral makeup. Still, even 500 years should be enough. Imagine all that has happened in Europe - or anywhere else in the world - during the last five centures, or even the last two centuries. The fact that we are all related does not mean that we are all the same (i.e. boring and generic) or that our histories are identical.
Secondly, so what if our ancestors in 5400 BCE are also the ancestors of everyone else alive today? Does this fact make their lives any less interesting? If anything, it should make them more interesting, because it means that whenever we read about events in this ancient time (and earlier), we are actually reading about our own ancestors. World history, then, becomes not just a collection of illustrative examples or a tale of "Great Men". It becomes our very own family history.
The revelation that "we're all related" is cause for celebration, not disappointment. It should bring us closer together as human beings, and make us more interested in our shared history, just like a group of cousins marvelling at their great-great-grandmother's life.
Those are my thoughts for the day.