DNA evidence seems to suggest that Neanderthals died out before ever contributing to our gene pool. Note that of course this is still being debated.
Neanderthals and mtDNA Finding out about our most recent common ancestor relies solely on inferences from the mtDNA of people living today. What if we could actually compare our mtDNA with mtDNA of a distant ancestor? This, in fact, has been done, with mtDNA from the bones of Neanderthals. Comparing mtDNA of these Neanderthals to mtDNA of living people from various continents, researchers have found that the Neanderthals' mtDNA is not more closely related to that of people from any one continent over another. This was an unwelcome finding for anthropologists who believe that there was some interbreeding between Neanderthals and early modern humans living in Europe (which might have helped to explain why modern Europeans possess some Neanderthal-like features); these particular anthropologists instead would have expected the Neanderthals' mtDNA to be more similar to that of modern Europeans than to that of other peoples. Moreover, the researchers determined that the common ancestor to Neanderthals and modern Homo sapiens lived as long as 500,000 years ago, well before the most recent common mtDNA ancestor of modern humans. This suggests (though it does not prove) that Neanderthals went extinct without contributing to the gene pool of any modern humans.