I have the iPhone 5 and these are the apps I am currently using that are

Health integrated:
- Fitport (on the iPhone 5, steps and other features have to be inserted manually)
- MyFitnessPal (insert your meals and calculate your calorie intake)
- FitStar (Virtual PT)
- Human (Registers time, distance and calories spent on activities such as walking, running cycling or exercising)
- Omvana (Meditation app, uses heart rate and other info to suggest appropriate meditation)
- MotionX (Sleep Monitor, Step calculator, Heart Rate measurement)