Here are some of the usage and downloads stats from the first week from my app Space Hops. Space Hops became available on the App Store February 15. Being my first app the results are better than I were expecting, especially since I did very little marketing.
The stats come mostly from Flurry Analytics. It is easily integrated by downloading an SDK and by adding just two lines of code.
The downloads stats come from iTunes Connect. There were over 100 downloads on the first day, with the majority coming from the US, then China, then Canada. On the first day I posted it to several iPhone Development and App forums, Tweeted and posted links to Facebook. The downloads steadily declined, but seem to have averaged out at 10-15 per day, mostly coming from North America. I am now a little over 350 downloads.
The number of sessions peaked on the second day, declined, then seemed to average out again and now I am seeing between 40-60 per day, but slowly declining. As of February 26 I have over 1100 sessions, with the median session being 60 seconds in length.
The following graph is the total time spent in the app by users. As of February 26, almost 27 hours have been spent in my app, which I am impressed by.
It was predictable that most download would come from North America, but I am pleased to see how many different places Space Hops is being played in.
Probably the age trend would expect for most casual games.