This website introduce 7 different solutions. Personally, I only have experience with Flurry and Google Analytics. I'm very pleased with Flurry and even though some of the other services also look good, I feel no need to try them. (This is not a review, only a recommendation...)
The API is super easy to install and use and compared to Google Analytics which is originally made for webpages and not really adapted to mobile apps, Flurry is designed for mobile apps. For example, if you use a UITabBarController or UINavigationController, you can with one line of code in your app delegate track all "page" views controlled by that controller.
The free analytics package is all you need to get all plenty of feedback on how your app is doing out there.
Check the webpage by clicking the logo above for more information.