One of the great things with the European Union is the right of free movement. As a EU citizen, you can live, study and work in any country within the European Union. This right does also include your close relatives – spouse & children – even if they are non-EU citizens.
However, if you are planning to neither work nor study in Sweden, you might have to prove that you have the sufficient means to support yourself during your time here.
Another good thing to know is that you are entitle to permanent uppehållsrätt, PUR, when you've lived and worked in Sweden for five continuous years. This right also includes your close relatives, if they lived with you during this entire time.