I can't speak for all of the SEC but for Tennessee, here are our rivals:
1. Alabama - This rivalry hasn't been very competitive lately but they are one of our biggest historical rivals and as we saw last year, it is still very intense for both groups
2. Kentucky - This is bigger in Basketball than Football but there are a lot of connections. I would claim Kentucky as Tennessee's second most important rival, especially if you look at all sports. We have also played Kentucky more than any other team and it is in the top 25 when it comes to most played rivalries all-time
3. Vanderbilt - In-state rival and the team we have played the second most. It isn't as big as other games because of the smaller fanbase of Vandy and their historical lack of success. They have won many games recently over Tennessee if you look at last 10 years (although TN has won 4 straight games).
4. Florida - Just football, this would be #2. It is a very tough rivalry because it is more famed for Florida being Tennessee's kryptonite and the fact that Tennessee seems to not do well in this game. Even last year, the game was far closer than it should have been.
5. Georgia - This is more of a recent rivalry but there seems to be a lot of hate here. If the divisions were not breaking up, I would say this would quickly become the SEC East game
6. Auburn - This was once a bigger rivalry but realignment ruined this one. Fanbases still hate each other. Just ask
@Wild Turkey what his opinion is of Tennessee
7. Ole Miss - Another annual series for Tennessee broken up by realignment. Frankly, this rivalry is dead and probably shouldn't even make the list
8. Memphis - Bigger in Basketball but a fun in-state rivalry
9. UCONN - Primarily Women's Basketball and really not the same with Summit's passing.
10. LSU - They really don't like us either but I think it is because we are both good SEC programs historically
11. Arkansas - There was a lot of coaching connections between Arkansas and Tennessee. The 1998 and 1999 games were very exciting and impactful.
12. South Carolina - In reality, not much of a rival but we are in the same division and it always tends to be a close game. I am not sure either fanbase would call it a true rival but then again, if the scheduling rumors are correct, apparently they will be one of our three permanent opponents
13. Texas - Not much of a rival now but I think this one has potential when they join the SEC. It can be called the battle of the UTs. There is a lot of historical connections between the two states, both schools are orange and white and call themselves UT. I just get a vibe that this one is going to take off