I am often asked to list the best rivalries in college football. My list is probably about the same as yours: Georgia-Florida, Texas-Oklahoma, Ohio State-Michigan, Alabama-Tennessee, Miami-Florida State.
I always leave out Alabama-Auburn and so the question is inevitably asked about the omission. Why do I not list Alabama-Auburn? Because, in my experience, Alabama-Auburn (or Auburn-Alabama) is much, much more than a mere football rivalry. It is a cultural war and the participants just use football to fight it.