Alabama is the constant, historic rival obviously... but I grew up and started watching college football in a time when UT OWNED 'Bama, so it didn't really mean that much to me, just another W. Florida was the game I looked forward to the most and wanted the Vols to win... obviously because they didn't do it very often in the Spurrier Era in Gainesville.
But with Spurrier gone, losing to the Tide a couple of times in the last few years, and learning more and more about the history of the programs, I can say personally that I'm starting to hate them more.