I was at a poorly attended Nats game last month. While the game was boring, the experience was made infinitely more fun when we played my favorite game to play while watching the game: Pass the Cup, Ante Up!
In Pass the Cup, everyone who wants to "play" (usually the members of a row, or your group of friends) all put in a $1 into a (dry) beer cup. After the 3rd out of each half inning, the umpire throws a new ball back to the mound. If it rolls up onto the mound and stays on the dirt, whoever has the cup keeps the $ in the cup. If it rolls onto the grass (usually does), you pass the cup to the next person in the line who holds it until the next 3rd out is made. The best part is when you have 10 people playing, even in the most boring game, there's a collective... uuuuuuUUUUUGGGGHHHH.... AAAHHHH!!! as the ball stays or rolls off. Awesome.
So what games do you play when you're at the game? We're going to be headed to a few this fall; we'll try your recommendations and report back.