I've heard they aren't terribly reliable either, but I know a few adopted people who have swabbed their cheeks and later declared themselves Native Americans, even of specific nations. There's one man who claims to have found his birth family using some mail-order DNA test. I don't know the story, but I think he must have been fantastically lucky.
Errm, this is not a question of DNA tests being unreliable, though. For what they *can* provide, the tests are reliable enough.
What isn't reliable or accurate is the companies selling these tests and the claims and promises they use to sell their tests with. At least this is the case in Europe, but I assume marketing and advertising strategies will not differ all that much. Ads promise the test will tell you which ethnic groups or even religious groups your ancestors came from (e.g. the claim the test was in a position to establish whether your ancestors were Jewish...).
One company selling these tests in Europe, and advertising quite aggressively, is situated in Switzerland, but apparently they are owned by a US company. The Swiss lot have a bad reputation for transfering personal data and test results (which will not be anonymised) to their US mother.
As far as I know, the tests use either mt-DNA or paternal DNA and establish the respective haplo group of clients. Therefore, they cannot fully establish ancestors in the first place, which is what clients also do not get told. Testing mt-DNA will only tell you which maternal ancestors can be established. Of course the test cannot tell any person what ethnic group their maternal ancestors belonged to – what they can tell you is where a particular mt-DNA type is found often. The individual DNA-types and subtypes have been recorded sufficiently so it is well-known at which point in time the particular subtype originated and in which region. If a company promises to tell you more – save your money.
Googling the Swiss company, I also found sites saying the Swiss company reduced the number of possible ethnicities in accordance to their US mother, as apparently they previously had too many names of ethnicities the usual Joe Public client in the USA was not familiar with. One site mentioned the company was now only using „Vikings, Germanic, Celtic, Basque, and Jewish“. For starters I'd like to know whether they mean to imply Vikings weren't a Germanic speaking population... Then I'd like to know what ethnic background they may tell clients who are from migrant families.
The company also promises clients to tell them which country their ancestors lived in 40 generations ago which they say is 10th/11th century. I'd like to know which country they will then allot to persons they label as of „Viking“, „Celtic“ or „Germanic“ ancestry. Do they opt for the simple solution? Something like Viking = Sweden, Germanic = Deutschland über alles? And I'm simply dying to learn which country they will choose for a client with a „Jewish“ haplogroup.
Promising clients to be able to use test results to find one's family, or even link them with family members etc, is highly dubious, to say the least, and at least comes pretty close to fleecing the customers. There is no shortcut to completing a family tree.
Claiming to be able to tell them which ethnic group clients come from falls into the same category. There are no „English“ genes, or „French“ genes, nor are there "Lakota" genes or "Quechua" genes, or whatever. That's all bogus.
I just had a look at the site named above, ancestryDNA. They promise you can find out whether you are part Irish, or part Native American. Nope. Their test will not be able to establish that. They can only tell you that the haplogroup that happened to be handed down in your line of ancestors happens to be frequent in this or that region of the world today. This doesn't tell you anything about the rest of your ancestry which - as far as the test result is concerned, since this rest does not show up in your haplogroup - may have been little green people from Mars.
Save the money for a better purpose.