As an undergraduate, should I have done research on all of my research interests listed in my resume? I am an undergraduate student, writing my resume for application to grad school.
During my undergrad I have done research on some topics through internships and research projects. However, there are also some interesting research topics that I have read about them and explored their goals in research groups' websites, but have not done research on them myself. These subjects are among my interests to pursue in grad school. 

Can I list them in the Research Interests section of my resume? I mean, is it necessary for undergraduates to have done research in all of their research interests when applying for graduate school?
Yes, include potential research interests that you are interested in and not just those you have participated in. Graduate schools like to know your goals and where you want to go with your graduate degree, so including what research would be interesting helps them know if they have faculty that can guide you in that direction.