It's a baseball blog, so this might be a dumb question.
I keep score at every Rockies game I go to (typically). I fault my short attention span. It helps keep me in the game.
It also gives me all kinds of nifty memorabilia to take away from the season with me.
I've started making my own scorebooks every season rather than buying the scorecard at the game; it saves me money and I can customize it as well.
I think it's a great way to enjoy baseball, but you gotta know how to do it, first. Take the poll and answer the question, "Can you keep score?"