Question

Is it possible to determine when a user first purchased your application? (Not just when they last downloaded it, hopefully device independent)

Answer 1

You could store the first run into the NSUserDefaults, the only problem with this approach is if they delete and reinstall the App you would lose the data:

NSUserDefaults *defaults = [NSUserDefaults standardUserDefaults];
[defaults setObject:[NSDate date] forKey:@"FirstRun"];