I'm not a compulsive app closer but my partner is. According to Mac blogger and publisher John Gruber, the practice of manually "killing" apps when they are in the background is counter-productive. He also says that Apple's approach to managing processor and memory with inactive apps is one of the iOS' big advantages over Android.
According to Gruber quitting applications that are in the background with iOS is actually detrimental to battery life and performance.
Apps in the background are effectively “frozen”, severely limiting what they can do in the background and freeing up the RAM they were using. iOS is really, really good at this. It is so good at this that unfreezing a frozen app takes up way less CPU (and energy) than relaunching an app that had been force quit. Not only does force quitting your apps not help, it actually hurts. Your battery life will be worse and it will take much longer to switch apps if you force quit apps in the background.
The article also points to some benchmarking that's been done to demonstrate how effective Apple's approach is when it comes to handling background apps.
The main reason I don't close them is that I can't be bothered. I use my iPhone a lot. If I stopped to kill apps after using them I'd waste a bunch of time.
Are you an iOS user that closes apps when you're not using them? If you are - why? Is there are a reason other than saving battery life for doing this?