I liked the A's when I was about 4 when they had Canseco and McGwire. But, I don't really consider them my second favorite team anymore.
I started liking the Marlins in the middle of last year, before I even knew what was to come in the playoffs, just cause they were a fun team to watch.
Other than that, any team that is an underdog or is fun to watch I will cheer for. But no one even comes close to the Chicago White Sox!!!