Have to beat : Tennessee Fun to beat : Auburn Recent rival that brings out the most fun/booze/tailgating: LSU
That sort of playful indifference could lead Auburn to switch conferences in search of meaning! I assume you're asking the charter members since they actually have rivalries with teams that weren't assigned to them by a committee?
A college football fan would say: Georgia/Florida Tennessee/Alabama Tennessee/Kentucky Alabama/Auburn Miss./Miss. State Arkansas/LSU Vandy? South Carolina? Texas AM? Missouri? Then I would say Alabama and whoever they are playing, like Texas every team that Alabama plays circles the game on the calendar. I can't say the same thing about any other SEC team.
I'm telling you Squall, you better back off. They will bravely run away and leech on to someone/something else if you don't make them feel a bit more relevant.
Fans of Georgia Tech, Tulane, and Sewanee University are welcome to join this discussion as well: they were also charter members of the SEC back when it was formed in 1932.