Denmark - House rental
Landlords generally prefer to rent properties to companies rather than individuals, so if your company is willing to sign the rental agreement you will find that landlords are more forthcoming.
It is possible though to rent an accommodation in your name. To sign a contract you need a valid passport as identification and three months rent deposit (this amount will not count towards rent).
The landlord will register your home country address in the contract. It is a standard danish rental contract, unfortunately only in danish. If you use a relocation company they can translate the main important points for you.
Note: Any deviation from the standard contract conditions, as for example the possibility to "break the contract" in case of transfer out of the country, must be noted in the §11 as diplomat klausul.
The real estate fee is normally paid by the landlord, which makes less interesting seeking to rent apartment from individual; in fact unless you have a good knowledge of Danish and Danish law it is not advisable to resort to the DIY route regarding renting an accommodation.