How to determine iOS app usage frequency for iPhone or iPad
I think I may have found an astoundingly low-tech solution to this problem, and it was right under my nose.

Ever since iOS became "multi-tasking" capable (I say that tongue-in-cheek, as we all know that most apps that get backgrounded aren't still running, they've just had their state saved until used again), the Task Switcher, accessible via a double-press of the Home Button, shows you a more-or-less "use-ordered" list of your apps.  Unless you deliberately open the Task Switcher and kill the apps, they linger in there... I guess forever, or until you reboot the device.

So, if I clear all those out, and then just go about my business using my device for a while, and occasionally look at what apps are in my first 3 or 4 "pages" in the Task Switcher, that gives me a decent idea of which apps I use the most-- or at least can tell me the ones that I've used "most recently".  Those apps that are on the far right "page" of Task Switcher are the least used (or at least the ones that were used "least recently").

EDIT: As of iOS9, the order of applications displayed in the Task Switcher is reversed.  The most recently foregrounded app is on the far right.

I suppose a person could extend this into a true exercise in statistical geekery by noting the order of the apps on a schedule... say every morning or every evening (or more or less often)... over a period of time; a week, a month, whatever.  Then you could compile that into useful info for yourself.