Texas was the biggest Hog rivalry back in the SWC days. Obviously, not how the Horns view it but that's how the Hogs saw it. Now in the SEC, I'd say LSU or Ole Miss are the biggest rivals and again, not how they view it.
The Hogs lack a true rivalry where the opponent view them also as their #1 rival. That sucks but the unfortunate truth with the geography and the lack of our sustained success.