Although the Vols are who I follow most closely, I have to start with a different team for the chronology to flow correctly:
UNC - Grew up outside of Charlotte and, as the song says, I'm a Tar Heel born and a Tar Heel bred.
UT - Moved from NC to Tennessee in 1990 as I was going into 9th grade. Being a Tar Heel fan was useless when it came to football (the running joke as a kid was that they were changing the name of the 7-Eleven convenience stores to 1-Eleven in honor of Carolina football!). So, once I got to this area, UT football was a natural draw. And, Peyton graduated high school the same year I did so it was fun to watch him since he was my age. I live and die with UT football now and follow it much more closely than even UNC basketball.
MLB - Dodgers. In 1986 my little league team was the Mets and that's the year they won the world series. Darryl Strawberry was my favorite player. Meanwhile, my dad was born and raised in LA and, naturally, has always been a Dodgers fan. So, when Strawberry was traded to the Dodgers, that sealed the deal for me. Been a fan ever since.
NBA - Like Panthro, I was a Hornets fan until they became the Bobcats. Since they are the Hornets again, I might get back into them if they ever have a decent team (if Jordan can become a good GM). Other than that...who cares? I'll watch some in the playoffs, especially if there is a player I followed in college (i.e. I'll watch the spurs in the playoffs to see if Danny Green does something good, etc.).
NFL - Peyton. I had moved away before the Panthers came around, liked the Titans when they were good. Like many have said, I don't know if I'll follow it or not once Peyton calls it quits.
Golf - The first player I liked to watch was Greg Norman. Now, it's Mickelson...the anti-Tiger! None of the young-guns seems to draw me in like either of those two. If Mickelson isn't in contention I usually quit watching.
Nascar - Don't watch at all. Growing up, we went to both the Charlotte races (spring and fall). We'd check-out of school early on Friday and camp in the infield all weekend. In those days, Harry Gant was my guy. That September when he was four races in a row (or maybe it was three of four races) was probably the last time I watched at all.
Hockey - I'll watch an overtime game in the playoffs if I stumble upon it.
Soccer - I'll watch the US in the world cup.
5 points extra credit for anyone who read all that!