How do I disable the navigation bar shadow in iOS 6 for navigation bars with custom background images?

Place this in your AppDelegate

[[UINavigationBar appearance] setShadowImage:[UIImage new]];
// is IOS 7 and later
[[UINavigationBar appearance] setBackgroundImage:[UIImage new] forBarMetrics:UIBarMetricsDefault];

Swift version with updates from comments

    UINavigationBar.appearance().shadowImage = UIImage()
    UINavigationBar.appearance().setBackgroundImage(UIImage(), forBarMetrics: .Default)