Lavie sez, "The Apex Book of World SF is the first anthology of SF/F/H stories from around the world, including Yang Ping's tale of Chinese hackers in a future game world, Aleksandar Ziljak's Men in Black meets Boogie Nights thriller and S.P. Somtow's classic examination of post-World War II Thailand and its most notorious serial killer. This rare anthology of international SF sets out to showcase some of the best international writers have to offer and the different perspectives of people from outside the American-British sphere of publishing - with authors from Malaysia, China, the Philippines, Israel and Palestine, France, the Netherlands and elsewhere."
The Apex Book of World SF (Amazon)
Apex Book of World SF Released! (The World SF News Blog)
(Thanks, Lavie!)

This looks very good, but in what sense is it "the first anthology of SF/F/H stories from around the world"? I'm pretty sure there have been a few others over the years.
I have this feeling too, but I couldn't name one. Can you list any other collections/anthologies that collect entirely (or largely) non-Anglo science/speculative fiction? Most collections I can think of that focus on diversity such as _Dark Matter_ and _So Long Been Dreaming_ feature mostly North American authors writing almost entirely in English.
Years ago I read a Russian scifi anthology that had a story involving butterflies that flapped their wings in sync with the queen butterfly, and a man trapped in a cave sent out a message via morse code by manipulating her wings, and another story involved a man who invented a machine to remove all the dust from the Earth, and all the atmospheric problems that caused. Wish I could remember the title.
Oops, my bad - it should be (as in the second instance) a "rare" anthology, not "the first" anthology.
There have been a few - Fred Pohl even released one issue of an international SF magazine back in (I think) the 60s. There was also a Hartwell anthology in 1989, and I'm pretty sure Aldiss and Harrison had one, but I can't find a reference online.
That was Lavie, sorry. Not having a good Internet day!
I should add there were also country or region-specific anthologies - a Chinese one in the 1980s, at least a couple of Russian ones, one on Latin America and so on. Spinrad and Wood were involved in doing a couple of Romanian anthologies in English in the 90s, but these were published only in Romania, as far as I know (which is where I got them). There's the SFWA European anthology, of course. We try to cover anthologies over at the World SF News Blog - I think Charles is actually compiling a list, so we post links and covers and so on when possible.
There's more in other languages - particularly the annual Utopiae anthology in France (published to coincide with the Utopiales festival in November) and there was a very interesting Spanish anthology a couple of years ago tied in with Hispacon that included several Arabic SF writers amongst other international writers.
In case anyone is interested, The Science Fiction and Fantasy Translation Awards is expecting to start up in 2011, and should be a good resource for translated F/SF
For those of you interested in SF from Germany and Austria, you should check out the anthology "The Black Mirror and Other Stories", edited by Franz Rottensteiner, which was published a couple of months ago.
http://www.amazon.com/Black-Mirror-Other-Stories-Anthology/dp/0819568317/ref=sr_1_4?ie=UTF8&s=books&qid=1257862512&sr=1-4
Speaking of Fred Pohl, he does a great blog:
http://www.thewaythefutureblogs.com
I just finished reading a library copy. Great stuff!
Here you go...
http://www.amazon.co.uk/Penguin-World-Omnibus-Science-Fiction/dp/0140080678/ref=sr_1_4?ie=UTF8&s=books&qid=1257882741&sr=1-4
WOA!!! The world outside the English speaking world...
In Russian check out these books by Sergei Lukyanenko
Dosori(Watch) Books:
Nochniy Dozor (Nightwatch)
Dnevnoy Dozor (Daywatch)
Sumerechni Doroz (Twilight Watch)
Posledniy Dozor (The Last Watch)
Labyrinth of Reflections Series:
Labyrinth of Reflections
False Mirrors
Transparent Stained-Glass Windows