While I have enjoyed the 5 pages of back and forth, trends in "rivalries" and reminiscing of the good old days like Kerwin to Quez to beat Lsu, I think we've over complicated this list. It's very simple. Our bitterest rivalries have to have become that way over time, have to be in close enough proximity to consistently interact, and had to have cost us something repeatedly. Therefore, the only logical names are as follows:
Tier 1
uga--there's no other team that truly fits the trifecta like the dogs. Absolute hate is justified.
fsu--they don't have the same length of time as uga, but have done an impressive job of cramming as much nastiness as possible in just 40 years. Again, hate totally justified.
Tier 2
Younger Gators will say ut, older ones will point to Aub. To be clear, they both suck. But technically the tigers have spoiled many more seasons than the vols, even since 1990. As was pointed out, minus a few years in the 90's, when we've lost to ut it's been entirely self-inflicted(3 of the 7 losses since '90 were against Zook or Mac). Auburn simply had our number for several decades, and was always that that you were concerned about. A third team that could make this tier is miami. It's as nasty a rivalry as we have, and I'm in the camp that is wished we just wouldn't play them at all. They haven't cost us anything necessarily, but have been a thorn in our side for a long time and are pure garbage.
Beyond that, I really don't hate. Lsu is as close to true hatred as it gets, but is ironically also a team that I don't mind seeing win in certain cases. Again, they've never cost us anything. It's maybe our most bizarre rival in that other than playing every year as a permanent crossover, there's no real reason for animosity. Alabama is nothing. Ohio State is a pasty nothing. Really neither have any business in a hate conversation.