I can’t think of any non-Canadian/American stand-up comics. There are myriad puveyors of raconteur drollery, slapstick comedy and pantomime absurdity in the ex-American Anglophone sphere, e.g., Quentin Crisp, Benny Hill and Monty Python, but I can’t imagine any one of them surviving Open Mike Night. And what about non-Engish speaking countries?
It’s hugely popular in the UK and Ireland. ETA: with dozens and dozens of native artists. Ever heard of Eddie Izzard? Billy Connolly? We get some US standups over here - Chris Rock’s latest tour was a sell-out, and Rich Hall has emigrated to the UK permanently - but the majority of the talent is homegrown.
No, it is not. The fact that I can’t name more than a handful of American stand-ups but many British ones doesn’t demonstrate that it’s an obscurity in America. It just tells you about my background.
I can think of more famous Irish stand-ups than Americans. And that’s not even a whole little island. But I can imagine that there might be more American stand-ups than I can recall.
So, no. Of course not.
American Jews invented it, and much like American Blacks with jazz, have some primacy in the field even today.
Comedy Central had a show called World Comedy Tour, which was filmed in Australia and featured a large number of Australian stand-ups.
Stand up comedy is one of those American favorites that has been exported everywhere. The culture of comedy clubs doesn’t translate well into every country, but there are certainly some equivalent venues that comedians can operate in.
Comedy is usually about observation and familiarity. You’re not going to get the jokes and flavor of a Japanese stand up even if he or she could speak English well enough to do the comedy. There will be few stand ups who will go over outside their cultures. Heck Larry the Cable Guy doesn’t go over well outside his culture. 
Something that jumps to mind while reading this is the Japanese Manzai style of comedy: it started as a more generalized performance art in the 1000s, but during the 16th-18th centuries it began to focus more heavily on purely comedic elements, and the modern incarnation is entirely comedy.
It’s a pretty neat formula, too: most manzai sketches feature lightning fast banter between two performers, a tsukkomi, or straight man, and a boke, or stupid man. The entire routine is based around the performers having a conversation in which they repeatedly present different viewpoints, and a lot of the humor is derived from the boke making mistakes which the tsukkomi angrily corrects. A lot of the humor in good manzai routines is derived from the quick succession of double-talk, puns, and other wordplay that is extremely tough to translate into English, but it seems like a reasonable analog to stand up that was derived from a non-european/north american source.
Oh, and if people are interested, this is an example of two people doing a manzai routine. The performers are called the Two Beats, and they ended up becoming absurdly famous for their various duo and individual comedy.
ED: Oh yes, I forgot to mention it but the performer on stage right is Takeshi Kitano, who plays the boke. His extremely bizarre take on things is necessary for the comedy to work, which is why he talks so much in the beginning.
“In Russia…”
See this earlier thread: “There’s no stand-up in France.”
Last Comic Standing this season had more than one English/Australia contestant (good ones, too) and at least two of the ones who were on last time I watched were non-North American types.
Perhaps a reason for its established popularity in Britain is that it didn’t have to create a market for itself from scratch, but neatly fitted in with and evolved on from the native music-hall traditions.
There’s no stand-up in Viet Nam, or anywhere else in Asia as far as I can tell. I’ve seen stand-up performed by overseas-Vietnamese for other overseas-Vietnamese in the audience, but even that’s not very common. They seem to prefer sketch comedy, singing, and dance numbers.
There’s standup in Latin America. Andres Poveda does standup as part of his Poveda Show Jo!!, seen in Panama.
It’s not uniquely American, but it is decidedly American. It’s one of the few art forms the USA has contributed to the world along with Jazz, Funk, Soul, R&B, and bluegrass (but even bluegrass is kind of transmogrified Celtic music).
Also, I can’t remember which comedian said this, but Stand Up Comedy is also the only art form geared solely towards selling alcohol.
Interesting. So would the classic Who’s On First? (YouTube link - usual warnings apply) routine fit into the Manzai formula?
Could it be argued that Oscar Wilde was a stand-up comic? I know not all of his lectures were comedic- they ranged from aesthetics to public readings- but aside from his writings he was popular and highly paid for making people laugh. Charles Dickens was also said to be hysterical when reading some of his lighter writings (and terrifying when reading Bill Sykes).
Mark Twain was definitely somewhere in the ancestry of stand up comedy, and while he was American he was inspired by Dickens and other authors who read and performed their works.
Stand-up is huge in Denmark, so … no?
Stand-up depends a lot on the national sense of humour though- for example, Danish humour is often much darker and cruel even than British humour- so it stands to reason that not much of it is exported.
That’s interesting. I guess I always had the impression that Continental humor was a little more of an innocent and dorky “ha ha, I’m so funny, look at me such a happy go lucky fellow,” like Roberto Benigni. For the OP I was kind of picturing a guy like Benigni having a nervous breakdown on stage as he’s slaughtered by hecklers at a New York comedy club.
I can picture Wilde as a droll raconteur talking at an audience and making them laugh, but I have a hard time picturing him or Twain or Dickens having that kind of give and take with the audience that I find fascinating about modern stand-up comedy.
I would imagine that stand-up comedy stems from Vaudeville (in the US) and Music Hall (in the UK) which began in the 1800s.
I don’t know which nation started it first, though, especially the acts that can be recognisably considered the beginnings of what we call stand-up comedy today.