Tourists do not need a Norwegian identification number. However, you have to apply for an identification number if you move to Norway.
If you plan to stay in Norway for less than six months, you need to apply for a D-number, which is a temporary identification number.
If you are staying in Norway for more than six months, you need to apply for a national identification number. More information, as well as application forms, can be found on the Norwegian Tax Administration's website.