I always pronounce it "Coe-pen-hah-gen" because that's the way Danny Kaye pronounced it in the song "Wonderful, wonderful Copenhagen" in the Hans Christian Andersen movie. Funny how things like that stick with you.

I agree with those who say the Danish pronounciation is irrelevant. Unless you're going to be consistent and say "Paree," "Mehico," "Yerushalayim," "Mahskva," and all the rest, pronounce it as an English speaker would.