Did Neandertals and modern humans interbreed? Maybe or maybe not say Jeffrey Wall and Sung Kim, who argue in PLoS Genetics that two prominent studies involving Neandertal nuclear DNA are flawed. Their online article is available here. The abstract states, in no uncertain terms:

Two recently published papers describe nuclear DNA sequences that were obtained from the same Neanderthal fossil. Our reanalyses of the data from these studies show that they are not consistent with each other and point to serious problems with the data quality in one of the studies, possibly due to modern human DNA contaminants and/or a high rate of sequencing errors.

If your data is flawed, it doesn't matter how good your study is.