What makes a great rivalry? Is it pure hatred, is it regional based, or does it develop because the teams are fighting for the same goals? In the case of Tennessee football, all three factors come into play for different rivalries.
UT obviously technically has an in-state rivalry with the Vanderbilt Commodores, even if they own that program. The Vols also have a pure hatred for the Alabama Crimson Tide and Florida Gators, and both developed in a period where the schools were fighting for the same conference or division crown. Now the Georgia Bulldogs are part of that.