Now that we know that Neandertal-introgressed DNA had (deleterious) functional consequences for modern humans, I think we also need a study on "useful stuff" conferred by Neandertal admixture. So far, the Neandertal genome has been used (mostly) as our closest relative, in order to identify novel gene variants shared by all modern humans but absent in Neandertals: the goal is to find things that "made us special". Pickings of this search have been slim.
Doubtlessly, as we begin to better understand the genetics underlying positive human traits, some of these will end up having come from archaic humans. Neandertal admixture was a huge injection of "new stuff" into the Eurasian modern human gene pool, and there is every reason to think that even if the "bad stuff" outweighed the "good", there was still plenty of room for functionally beneficial variants to be acquired from them.
Science 12 Feb 2016:
Vol. 351, Issue 6274, pp. 737-741
The phenotypic legacy of admixture between modern humans and Neandertals
Corinne N. Simonti et al.
Many modern human genomes retain DNA inherited from interbreeding with archaic hominins, such as Neandertals, yet the influence of this admixture on human traits is largely unknown. We analyzed the contribution of common Neandertal variants to over 1000 electronic health record (EHR)–derived phenotypes in ~28,000 adults of European ancestry. We discovered and replicated associations of Neandertal alleles with neurological, psychiatric, immunological, and dermatological phenotypes. Neandertal alleles together explained a significant fraction of the variation in risk for depression and skin lesions resulting from sun exposure (actinic keratosis), and individual Neandertal alleles were significantly associated with specific human phenotypes, including hypercoagulation and tobacco use. Our results establish that archaic admixture influences disease risk in modern humans, provide hypotheses about the effects of hundreds of Neandertal haplotypes, and demonstrate the utility of EHR data in evolutionary analyses.