I believe Appannie.com is what you are looking for.

A number of app developers have shared a few of their experiences, metrics and numbers on Quora, so that would be my first suggestion. Denys Zhadanov and his impressive team at Readdle also publish stories on their company blog highlighting metrics that might be very useful considering their apps are almost always in the top 100.

Beyond that, I'd also suggest having a look at App Annie, which offers a continuously growing source of indexed app store / marketplace data for all apps. They also have a number of paid products and content depending on your need for competitive intelligence and insights on your own apps.

Their's no trusted source for knowing how many downloads a specific app has gotten only if the developers of the app publish some numbers.
However www.xyologic.com presents the number of downloads for a wide variety of ios apps in different categories but I'm not sure about its reliability.