Ø is only used in Danish and Norwegian to my best knowledge. The Swedes liked the German letters more, and therefore they have ä and ö instead of æ and ø (æ not to be mistaken for the French œ which is actually pronounced just like the Danish/Norwegian ø (and Swedish/German ö).
As you sometimes find yourself in a situation where you don't trust the special characters on your keyboard, you can use oe instead, which most people in all five countries understand (Oe in uppercase).
Another nice useless fact is that the word ø actually means island in Danish. And the danes actually have a meaning for the word å as well - which they share with the Norwegians AFAIR)