I was born in Arkansas and blessed to have good parents, so I have a natural hatred for Texas. However, the first program I grew to have a hatred for because of personal game experiences was Tennessee.
And it wasn't just because of 1998, though that certainly solidified it. I remember Peyton Manning converting 3rd down after 3rd down, and watching helplessly as the Vols staved off Arkansas' upset bid in Little Rock in 1997. It seemed like everybody hated Philip Fulmer, including the Tennessee fans who felt he stabbed Johnny Majors in the back.
Arkansas and LSU have a reputation now for playing classic weird games, but before that, Arkansas and Tennessee played each year from 1992 through 2002 in a similar string of memorable contests.