At least, those of us of European or Southeast Asian descent are, according to recent DNA evidence acquired by sequencing Neanderthal DNA.
There's also a brief discussion of the implications of this discovery on this Caveman podcast from To the Best of Our Knowledge*.
As a very small number of you may know, I've been playing around with the idea of Neanderthals and other ancient hominids assuming the roles traditionally played by mythical humanoid species in epic fantasy. I've explored the idea of interbreeding as a part of that, so this evidence interests me.
*(Following that discussion on the podcast, there's a discussion with archaeologist Brian Fagan about his recent book on Cro-Magnons that I found myself snorting out loud at, due to the utter confidence with which Fagan offered as factual statements a series of completely unqualified assessments as to how the art of the Cro-Magnons revealed the depth of their supernatural belief system and the showmanship of their rituals, in spite of the fact that he HAS to be INTERPRETING and investing with psychological and emotional signifance a limited set of ancient visual and physical evidence that is, by the way, completely lacking in either written records or any kind of explanatory oral history or myths that might actually reveal feelings that are otherwise lost to time. His ideas are interesting, and he may be correct, but what he's stating as facts are conjectures that can't be proven. As someone with an extensive scientific background, his abuse of this distinction between hypothesis and empirical fact was a bit startling to me. Hopefully the book is more nuanced.)