Interestingly, if you use 23andMe's genetic analysis service, it'll tell you how much Neanderthal DNA you have. The average European has 2.7% (I have 3.2%).
[0] - https://customercare.23andme.com/hc/en-us/articles/202904760...
[1] - http://www.isogg.org/wiki/Autosomal_DNA_testing_comparison_c...
(I will admit to not having compared more than a handful of SNPs with what 23andMe has to say about them, and I suppose they could have tampered with the data, but that seems like a lot of effort for the one-time payment they got from me...)