If you have taken a DNA test with Ancestry or 23& Me, if you download your raw DNA, you can upload you DNA to many sites. This site, http://genotation.stanford.edu/ , can tell you if you have some Neanderthal in you!
Here is where you can upload you upload your DNA file.
After Uploading it will take some time.
After a minute, you will see some thing like this
As you can see, I am a little Neanderthal.