Braves 50
Vols 23
Titans 23
MTSU 4
These are the only teams I care enough about to keep up with. But baseball (and the Braves) were my first love. My whole family are big VOL fans. Dad, sister, and brother are all UT alumni. I was the black sheep that went to MTSU to "get away." But I didn't start following football more than casually until I was about 10-11 when Peyton became a household name. A coulpe years later, we won the natty.
As far as the NFL, my family never had strong affliations to any team when I was growing up. We watched the Braves every Sunday afternoon on TBS, not the NFL. The Super Bowl was pretty much the only NFL football I watched growing up and my "favorite team" changed based on who was playing in the Super Bowl. I was a Cowboys fan for a few years, then I was a Broncos fan. When the Oilers relocated to Nashville, we started watching a little bit, but not significantly. Then I recall listening to the Music City Miracle on the radio while me and dad were cutting down trees and stacking fire wood. I felt the excitement from Mike Keith calling that play. I've been hooked ever since.
EDIT: I added MTSU to the list as well, because I do root for them to do well, I just don't follow them at all.