Yes you do, even as an EU-citizen you need to apply for residency if you wish to live for extended periods of time in Spain. EU and EEA citizens may live up to 3 months without the need to become a resident.

 As a non-EU citizen, you will be in one of two categories:

1. Without a residency card from another Schengen-area country: you will not be able to stay in Spain for more than 3 months per every 6-month period. This is irrespective of whether you come from a visa-free country (eg. U.S.A, Canada, Australia, Israel etc.) or you need a Schengen visa to travel to Spain.
2. With a residency card from another Schengen-area country: legally, the maximum stay period of a resident of a Schengenland country in another, is 3 months.

You can quickly and easily obtain one through the services of SpainResidency.com. We specialize in Investors Residency (“Golden Visa”), Non-Lucrative and self-employed work and residency permits.

In practice, anything between 10 and 90 days can be expected depending on the type of application, the Consulate you apply through and the Spanish province where you wish to reside in (some immigration offices are busier than others). 

Unless you are originally from a Latin-American country, Portugal or The Philippines, you will need at least 10 years of uninterrupted residency.  If you are from any of the former countries, you will need at least 2 years of uninterrupted residency. 

Specifically, Yes you can, in fact, it is normal for Non-Lucrative or Investors-Residency applicants to apply together with their families. Not only can Investors-Residency applicants bring their children under 18 years of age (or over 18 that are dependents), but also their parents provided they are dependents.