Paper Football HD
Free, although you can upgrade to a "premium" edition
The fun of most sports games is that we get to imitate the actions of athletes who are vastly more talented and skilled than we'll ever be. Whether it's catching a goal line fade pass, striking out a batter with 95 mph heat or hitting a buzzer-beating three-point shot, these games let us simulate the most exciting moments in professional sports.
Paper Football HD, on the other hand, lets us relive the excitement of an impromptu game we used to play in high school while bored in detention. The best part of this game is that it actually has a "premium edition" that you can buy for 99 cents, although its iTunes page doesn't spell out what new features you get for your cash. Maybe it simulates the experience of having classmates hurl spitballs at you.