Lots of feelings on this.
A true fan ...
Supports their team/school win or lose, no matter what the record.
If they live too far away to go every week, makes a pilgrammage each chance possible - game day or not.
Tells his fiance "I love you. But when (team/school) is playing, I'll be in front of the tv or the computer to follow the game. I need you to understand that before we get married."
No matter how bad things get for the team, a true fan holds out faith for next year. (Any true Cubs fan knows this).
Makes sure in every fantasy league, there is a representative of his favorite team on his squad. (For me, that means trying to get a Chief, and that's tough. Taking Keading, Clark and making a play for S.G. are easy)
Wears team gear after a loss, and doesn't give a crap what people have to say about it.
Develops a true hatred for a rival based on past sins, even if they did not occur in the fan's lifetime.