With some extra time on my hands was pondering the the companies that do research your ancestry and if it is available world wide.
Was thinking like if some armed service people who served overseas and messed around with the locals and now they get a phone call/message/letter saying “hi I’m Ton Chung and live in Viet Nam (or wherever) and you’re my dad!” Does this ever happen, or are these tests only available in the USA/North America?
23 is only available in some countries. If you go to the website, scroll to the bottom, and select ‘Change Location’ you can read about it.
Most of these companies are American, so it’s only natural that they would target primarily the American market. Of course they are also available in other countries (though relatively few, as the “choose location” tab on the23andme website already mentioned indicates).
This may have to do with legal implications, since the companies do get access to highly personal data which may be subject to restrictions as to how it may be processed in some jurisdictions. On top of that, there is, in my anecdotal experience, generally a higher degree of interest in genealogy among Americans than among Europeans. This may have something to do with the fact that Americans are more aware of the history of their country as a destination for immigration and a melting pot. Which is not to say that Europeans are genetically homogenous - events such as the Migration Period in the early Middle Ages have thoroughly stirred up the European gene pool. But those events are not present in people’s awareness; most Europeans don’t think of themselves as “Romanian French” or something analogous, just because they are descendants of some Hun from what is now Romania who came to France centuries ago, the way many Americans think of themselves as “Italian American” or the like.
To some extent, many of the current or popular genealogical research companies and websites exist wherever there are Mormons. Although companies like Ancestry are not owned by the Church of Jesus Christ of Latter Day Saints, the owners of the companies are often members of the church. Mormons believe in after-death baptism/conversion of your relatives, so they generally want to know as much as they can about their ancestors as far back as possible. Their companies provide a place where non-Mormons can do genealogical research, and they get access to the results of at least some of that research.
There are several of these DNA services by now; I think some can be accessed from anywhere.
Would you or your family want to know if there was such a connection? 
But you can avoid this by using a fake name with a throwaway email address when you apply. You’ll still need a debit card or equivalent and a real snail-mail address — (I suppose law enforcement might go after those with subpoena) — but those can also be faked with some effort.
I was thinking more along the “surprise I’m your child, half-sibling, etc…” that you or your family didn’t/wouldn’t know about. The kind of stories you read about in Dear Abby. All these I have read seem to be within the USA, just wondering of the possibility someone contacting you from 1/2 way around the world.
I have heard stories about servicemen serving overseas like during during the Vietnam war and had some “love 'em and leave 'em” relationships with the locals.
Also, with 23, you decide how much you want your information to be public. If you don’t want your relatives to see you (and you see them) do nothing, and your results are ’private’. If you want to connect, you select ‘share’, and you, well, share. And you select how much to share. you can also change those settings, minute to minute. I suspect (no cite) that all others will be the same
But, and this is a big but, if your close relations share, it might get back to you. Just sayin’.
The DNA testing on ancestry is just one small component. I did it but it didn’t say much more than what I already knew. Kind of cool seeing that I have some cousins all over the world. What is most useful is the access to documentation and records. And the ability to piggyback off the work others have done if they allow access.
Same thing with ancestry. Also on ancestry even if you have your tree public anyone marked as being alive will be shown as private.
Knowing where you “came from” is appealing in immigrant countries like the US and Australia. It has a limited appeal in Korea and Japan, for example, where ethnic homogeneity tends to go back a few thousand years. They already know where they came from.
The genealogical family-tree drawing aspect of these sites remains popular in Australia, and there has also been some advertising about finding your ancestry via DNA analysis. At the same time there has been quite a bit of negative publicity about the privacy implications about getting this done. Basically, if you were not aware, the fine print in the release essentially gives these companies ownership of your genealogical information derived from DNA testing. Why does this matter? Because your genetic predispositions to certain diseases may be worth a bit to someone else, like an insurance company or even for a direct-marketing pharma, it could be provided to the police in support of an investigation. Think of your mobile phone data, but even more intimate.
Two of the biggest players in the game are US companies. For Ancestry it grew out of their genealogy platform, whereas 23andMe primarily focused on “medical” advice. Both of them though have marketed the “ethnicity estimate” heavily, although that’s possibly the least useful or accurate part of what they offer. (23andMe’s medical advice is at least theoretically useful to a handful of their users)
The “ethnicity estimate” is much easier to sell to “melting pot” Americans. Genealogy is also, by percentage, a bigger hobby in affluent and “roots seeking” America than most of the world. So the largest pool of tests come from Americans.
That said, cites such as MyHeritage and FamilyTreeDNA have a much larger portion of European testers and there are similar companies that are popular in parts of Asia. And even if your country restricts DNA-testing there are ways to get around that, so yes, “your dad must have fathered my dad while he was in Vietnam”, or at least similar things, do happen, but they are much rarer than “I’m your distant cousin, do you know which cousin or ancestor of yours might have fathered children in XXXX”.