Just like the main app, Push-Up Wars allows you to enter and register how many push-ups you're doing each day, and then the app will track your progress both among your friends and on a global leaderboard level. Push-Up Wars is notable even if you're not an exercise fanatic, just because it's the first app I've seen that's not a game, technically, but still uses Game Center. You can earn ranks and achievements as you "level up," and then see global and friend-based leaderboards.
Registering push-ups requires you to take a video of you doing the exercise (only uploaded if you agree to do so), so the app requires a video-enabled iPhone or iPod touch -- no dice on older versions. But it's an interesting idea that's executed quite well, and if you want to get serious about powering up those arms, Push-Up Wars might be able to help.
Apple iPhone 6s