I had to change the type of fan I am though. I used to be the kind of fan that would show both really excited emotion and really bummed emotion during games. With kids, I had to just show excited emotion but more or less repress every urge to express frustration during games. If I'm visibly upset and grumbly, my kids don't really want to be around me.
I've actually come to enjoy games a lot more that way.
Also, we make a big deal of getting game day t shirts each year and we hike the Y several times each summer.
It also helps that my oldest is a boy and got the BYU football bug when he was 4. His name has a Y in it and by default he writes it like the oval Y as part of his name.