Requirements regarding passports and visa are not the same for EU citizens and non-EU citizens.

EU or non-EU citizens?
If you are an EU citizen, it is obligatory that you obtain either a valid passport or a valid ID card in order to enter and be in Denmark up to three months.
If you are not an EU-citizen, you must have a valid passport.

Both Ministry of Foreign Affairs in Denmark and Ministry of Refugee, Immigration and Integration Affairs have detailed guidelines regarding visa rules.