I am a biologist and have spent quite a bit of time teaching about DNA, chromosomes, crossing-over, introns and all the rest of the amazing science that has emerged in the last 60 years or so.
At the level of checking for non-paternity, DNA is pretty good: it's ever so good at saying that x person is not y person's child, or that the murder weapon was held by the alleged murderer, or whatever. I don't have a problem with that: it's hard-edged, yes-or-no stuff. Following the Y-DNA or mitochondrial DNA, which in general are inherited directly down the male and female line, has value in the same way, but it only touches one line in a family tree: father's father's father's father or mother's mother's mother's mother, and of course fails when there is an adoption, a fostering, a "non-paternal event."
Because of the rather fuzzier nature of the evidence (I'm tempted to put that as "evidence") of DNA analysis into the deeper past, I am much less certain of the value. If a test told me that I had 15% Viking ancestry or whatever, I'm afraid I'd be more likely to treat this in the same way that I'd treat a horoscope!
And - that's why I haven't bought a test....