As described in a recent Discovery News article, researchers have confirmed that part of the X-chromosome of all human populations other than sub-Saharan Africans comes from Neanderthals, solidifying earlier findings suggesting the likelihood of interbreeding between them and early humans. What this means is that every human being alive today who has any genetic contribution from outside sub-Saharan Africa is part Neanderthal.
While the findings are not a shocking revelation to the scientific community - the research behind them has been ongoing for years - it may be seen as significant in symbolic terms by the general public given the relative fame and emblematic nature of the Neanderthal in popular culture. Although commonly misunderstood to be a different species than humans, Neanderthals were in fact close enough genetically to breed with African humans who migrated outward later. From the Discovery News article:
The ancestors of Neanderthals left Africa about 400,000 to 800,000 years ago. They evolved over the millennia mostly in what are now France, Spain, Germany and Russia. They went extinct, or were simply absorbed into the modern human population, about 30,000 years ago.
Neanderthals possessed the gene for language and had sophisticated music, art and tool craftsmanship skills, so they must have not been all that unattractive to modern humans at the time.
I must admit, I find the idea that I'm part Neanderthal irrationally exciting. It's easy to intellectually appreciate being descended from various sources, but this seems somehow more specific and personal, like being introduced to a particular, demonstrable ancestor rather than having a given relationship tentatively surmised from the fossil record. This is one of the benefits of modern DNA sequencing technology.
Now, the fact that their DNA is present doesn't mean it remains significant to our biology today - it could just be a small contribution that occurred in a small population that subsequently happened to bloom into the majority of the species. So its importance is primarily in nailing down the phylogeny, which has apparently been accomplished with this finding.
A rather evocative, soulful interpretation of what a Neanderthal looked like (from the Smithsonian, credit to Andrew Griffith):