What is the maximum range one could travel with a single Portkey? Across the world? To the moon?
According to W.O.M.B.A.T., in order for portkeys to be arranged between countries, the consent of both Nations's Ministries of Magic may be required. (sourced from Wikia)
As such, you can clearly travel across long distances. Among the known uses:
France to Burrow (implied, there's a chance it was not a direct transport)
Mr. Weasley had therefore gone to meet the Delacours on top of a nearby hill, where they were to arrive by Portkey (DH - Ch 6, "The Ghoul In Pajamas").
Godric's Hollow to somewhere in Europe (wherever Grindelwald's home was)
“It was poor little Ariana dying, I think, that did it,” says Bathilda. “It came as an awful shock. Gellert was there in the house when it happened, and he came back to my house all of a dither, told me he wanted to go home the next day. Terribly distressed, you know. So I arranged a Portkey and that was the last I saw of him (DH - Ch. 19, The Life and Lies of Albus Dumbledore.
I was unable to find canon information beyond that, in the books, Pottermore or interviews (or Wikia :).
The answer from @DVK shows that Portkey travel can be international, but all his examples remain within Europe. The following quote gives us an example of what is probably inter-continental Portkey travel:
"While there have been no proven referee slayings since , there have been several incidences of broom-tampering over the centuries, the most dangerous being the transformation of the referee's broom into a Portkey, so that he or she is whisked away from the match halfway through and turns up months later in the Sahara Desert."
-- Kennilworthy Whisp, Quidditch Through the Ages
It sounds as though Portkey travel to the Sahara Desert was done multiple times from multiple different Quidditch pitches, presumably not all in Africa.
(This is the longest Portkey trip mentioned in the Wikia.)
While Rand al'Thor's answer mentions a case of what may be inter-continental travel, the quote he brings can be interpreted in other ways.
In the following Twitter exchange, however, J.K. Rowling clearly implies that portkey travel is possible between the U.K. and America (across the Atlantic).
Loved the movie. Burning Q from my wife though: How come Newt travels by boat to cross the Atlantic instead of apparating?
J.K. Rowling: There's a limit to how far you can Apparate. Inter-continental Apparition is very dangerous!
Why couldn't Newt have used a portkey? It can't have been difficult for him to register one since he works at the Ministry.
J.K. Rowling: Consider the effect on the contents of his case...
Rowling shows that while Apparition has distance limits, portkeys do not.