NSUserDefaults в помощь
Update:
func application(application: UIApplication, didFinishLaunchingWithOptions launchOptions: [NSObject: AnyObject]?) -> Bool {
...
let userDefaults = NSUserDefaults.standardUserDefaults()
if var numberOfLaunches = userDefaults.objectForKey("numberOfLaunches") as? Int {
numberOfLaunches++
userDefaults.setInteger(numberOfLaunches, forKey: "numberOfLaunches")
} else {
let n = 1
userDefaults.setInteger(n, forKey: "numberOfLaunches")
}
print(userDefaults.objectForKey("numberOfLaunches") as! Int)
return true
}