Portkeys - yes.
The answers to this question show that Portkey travel can be international. Copying quotes from my and DVK's answers over there:
from various places to the Sahara desert:
"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
from France to the Burrow:
Mr. Weasley had therefore gone to meet the Delacours on top of a nearby hill, where they were to arrive by Portkey
-- HP and the Deathly Hallows, Chapter 6: The Ghoul In Pyjamas
from Godric's Hollow to eastern Europe:
“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
HP and the Deathly Hallows, Chapter 19, The Life and Lies of Albus Dumbledore
Apparition - usually no.
The answers to this question show that there is some confusion and contradiction over whether or not Apparition can be international. Firstly, as stated in KeithS's answer, this quote from the books tells us that there is a limit on the distance even a skilled wizard can Apparate:
Harry knew it; his scar was bursting with the pain of it, and he could feel Voldemort flying through the sky from far away, over a dark and stormy sea, and soon he would be close enough to Apparate to them, and Harry could see no way out.
-- HP and the Deathly Hallows, Chapter 23: Malfoy Manor
The following quote from Kevin's answer tells us that it is possible but risky to Apparate across continents:
Apparition becomes increasingly unreliable over very long distances, and only highly skilled wizards are wise to attempt it across continents.
-- Quidditch Through the Ages, Chapter 9
And finally, Richard's answer tells us that Apparition between countries is banned.
Floo - unclear.
All the information we have in canon concerns the Floo Network within Britain. This includes the latest articles from Pottermore by JK Rowling. Quoting from the second of these sources:
Floo powder was invented by Ignatia Wildsmith in the thirteenth century. Its manufacture is strictly controlled. The only licensed producer in Britain is Floo-Pow, a company whose Headquarters is in Diagon Alley, and who never answer their front door.
The inclusion of the words "in Britain" would seem to suggest that there are Floo Networks in other countries too, but doesn't tell us whether they're connected.