This node exists primarily because I saw it hardlinked from this node by QXZ. I have, however, seen other people use it, which puzzles me.

The mistake is commonly perpetuated by English-speaking foreigners (other European or foreign countries have their own unique spelling of the capital) who, for one reason or another, will attempt to convey a certain air of authority where none exists.

I've been racking my brain trying to think of a suitable explanation as to why people would spell Copenhagen with an umlaut and found none. I have, however, been able to think up numerous reasons why Copenhagen should not be spelled with an umlaut:

• The city of Copenhagen is not really called Copenhagen anywhere except in English-speaking countries. In native Danish, it is called København. Most Scandinavian countries follow this pronounciation (with subtle differences, eg. the Swedish "Köpenhamn" - thanks, LX).
• The umlaut 'ä' is not a Danish letter. The Danish language does have three extra letters, where one of them is pronounced exactly like the German/Swedish 'ä'. It is, however, written 'æ'.
• The pronounciation is messed up with the introduction of the umlaut. Depending on where you're from, the word "Copenhagen" will be pronounced differently. Including an umlaut would force an extremely stressed American sound, ie. a very flat A (as in "pastry"). This opposes the British pronounciation, which is typically with a more open A sound (as in "cars").
• The English "translation" of København is probably derived from German "Kopenhagen" (the English merely exchange the 'K' with a 'C'). Additionally, the letter 'ä' does exist in the German alphabet. However, notice that even the Germans don't spell Kopenhagen with an umlaut.
• Lastly, and most clinchingly: The letter doesn't exist in the English alphabet. Using it in an English sentence exclusively containing English words is a literal fallacy. Instead, the word should be phonetically altered to suit the English alphabet - in this case, "Copenhagen".

So stop it. It's not making you look clever.