Where can I find statistics for most searched apps in the App Store? Does anyone know if it's possible to find out what people are searching for in the App Store?

I'd like to be able to pitch to a client that there is a high demand for a certain type of app. Is it possible to see this sorta like a Google AdWords Keyword Tool for the App Store?
Officially? You can't. Apple does not provide any specific metrics about apps nor searches except those provided in Keynotes (we have $x apps, paid $y to developers, etc.). You could really only make assumptions based off the list of "Most Popular" apps in the App Stores.

Your closest bet would be whether or not a third-party ad network like AdMob or LinkSynergy publishes statistics of their own. Their own scope will of course be limited compared to the overall searching traffic, but it may be as close as you're going to get.