1. Dallas Cowboys
2. Alabama Crimson Tide
3. Miami Hurricanes
Really it is Dallas and then nobody else... but in the spirit of the question, I'm pulling out the two teams I follow more closely than others.
Since I've lived in SEC country for so long now, I started watching Alabama when I was in high school and slowly have become a pretty big fan.
As for Miami... believe it or not I was a huge Jimmy Johnson fan since before he ever became the Dallas coach. When he was with Miami I was pretty young and loved the way his Hurricanes played the game. I became a big fan right away. I actually told some buddies that I would love for him to coach the Cowboys, but never thought it would happen. Needless to say, I was pretty happy when he was hired by Dallas.
When Jimmy was in Dallas, I kind of saw the college version of Dallas in the Hurricanes and just kept pulling for them. Still do.
I came by being a Dallas fan honestly though. Born in Dallas and my father would have kicked my tail if I would have pulled for anyone else. Silver and Blue since birth.
As for other sports teams... I really don't follow anything other than college or pro football, so... I got nothing for any other sport.