Here's a list of what I believe are the "flagship" state universities in each state. I'd love to hear corrections from people who better understand the situation in each state. I get the impression that the term "flagship" is supposed to indicate the state university that gets the most funding, is perhaps the most selective in admitting students, and is regarding as the top state university in each state. I suppose in some states it is debatable which university should be so designated, and maybe in some states there is more than one "flagship" university. I'll list links for some universities in some states I know. Please reply with additions or corrections based on your local knowledge.
University of California: Berkeley ("Cal" or "Berkeley")