A friend of mine recently took a DNA ancestry test using one of these mail-order services.
Sadly he did not provide the name of the company used.
According to his results, he has partial Native American ancestry.
Honestly, it seems exceedingly unlikely to me that a White Englishman with no known ancestral links to America would have Native American ancestry. I do not know what the historic Native American population of England and the broader UK is, but I am willing to bet that it was completely negligible in proportionate terms, and probably would have been clustered around the Court and high society in London, not in the provincial parts of Northern England that this guy and his family hail from. I am more inclined to be sceptical about the provenance of the companies providing these tests.
There are also various examples on YouTube of participants in chat shows being told that they have surprising ethnic origins on the basis of these tests. Usually these have a theme where someone expresses hostility towards a particular group, only to be shocked when - very conveniently - they turn out to be "17% Black" (in the case of a White American who allegedly expressed hostility towards Blacks) or "24% Indian" in the case of a Muslim Pakistani who expressed distaste for India. (as an aside, how could a test like this determine nationality, as opposed to ethnicity? From the little I know about the racial origins of the people who today are Pakistanis and Indians, there was considerable overlap - grounds for further scepticism).
How reliable are the claims of these tests and the companies who proffer them?