If you are asking about "The NFL" as opposed to "The Packers", my answer is "not very."
I find as I age, national/internationalpro sports in general matter less to me each year. It's too much business and too much marketing and too much economics driven for me. (Not that I dislike business and marketing and economics -- its a big part of what I do for a living, after all -- but I always liked sport as something "separate' from everyday life.
When I was young, we called it "extracurricular" activity, and that fits for what I want. I want something that I can turn off the real world and immerse myself in for its own sake. And pro sports just don't do that.
I still care about the NFL more than the others. But that's only because I still get that feeling from watching and following the Packers. If the Packers weren't there, I expect I would follow the NFL about as much as I follow the NBA, NHL, MLB, and Divsion I football and basketball (yes, Div I is pro sports, even if/when the athletes don't get paid). Which is to say, not much at all.
If it weren't for the Packers, I might occasionally avoid work by napping in front of the TV on Sunday afternoons. But that's about it.
And do not be conformed to this world, but be transformed by the renewing of your mind, that you may prove what is that good and acceptable and perfect will of God.
Romans 12:2 (NKJV)