Nordic citizens living in Sweden
If you are a citizen of Denmark, Finland, Norway or Iceland you may be considered both a Nordic citizen and an EU/EEA citizen, and use two different sets of rules.
Denmark, Finland, Norway and Iceland, along with Sweden, constitute the Nordic countries. The Nordic countries have an agreement which states that Nordic citizens have a right to live in whichever Nordic country they choose. You do not need to apply for a residence permit. If you want to live in Sweden you simply need to register with the Swedish Tax Agency.
If your family are citizens of a non-EU/-EEA country and you intend to live in Sweden, they can apply for residence permits in accordance with Swedish rules.
Moving within the EU/EEA
EU/EEA citizens and their families have a right to move to another EU/EEA country as long as certain requirements are met. An EU/EEA citizen has the right to live in an EU/EEA country which is not their country of origin as long as they meet the requirements for right of residence through work, studies or with sufficient means. In Sweden you simply need to register with the Swedish Tax Agency.
As a Nordic citizen you are also considered as an EU/EEA citizen. You do not need to apply for permits to live in Sweden. If your family are citizens of a non-EU/-EEA country they can live with you in Sweden as long as you have right of residence. In this case, your family should apply for a residence card in accordance with EU/EEA rules.