Just so we're all clear: Although it makes things visually neater to "close all," it has absolutely no effect on the phone itself -- though it might still make you happy.
The "recent apps" button merely shows those apps that you have accessed, regardless of whether they are running or not. "Closing" them out of that screen is merely a cosmetic change: it just drops them off this list of things you've accessed. Now, suffering from a certain amount of OCD myself, I understand why you might want to "close all" of those, but it won't change the operation of your phone one whit. (Though if you've been accessing a naughty app that you don't want anyone to see if they have your phone in their hand, this could make sense.)
If you want to "close" recent apps -- as in "stop them from running" -- you would go to Settings > apps and scroll right to "Running". Then click on the one you want to stop, and press the "stop" button. This may have very little effect, since a system service that's required to run will merely re-start itself. But if there's a rogue app that keeps running for no reason, by all means make yourself happy and stop it. What's the harm?
So, there's no practical reason to "close all." But if it gives you an emotional lift to empty out your list of recent apps from time to time, knock yourself out! Happiness is important!!
