registerForRemoteNotificationTypes: is not supported in iOS 8.0 and later

For iOS<10

- (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary*)launchOptions
{
    //-- Set Notification
    if ([application respondsToSelector:@selector(isRegisteredForRemoteNotifications)]) 
    {
           // iOS 8 Notifications
           [application registerUserNotificationSettings:[UIUserNotificationSettings settingsForTypes:(UIUserNotificationTypeSound | UIUserNotificationTypeAlert | UIUserNotificationTypeBadge) categories:nil]];

           [application registerForRemoteNotifications];
    }
    else
    {
          // iOS < 8 Notifications
          [application registerForRemoteNotificationTypes:
                     (UIRemoteNotificationTypeBadge | UIRemoteNotificationTypeAlert | UIRemoteNotificationTypeSound)];
    }

     //--- your custom code
     return YES;
}

For iOS10

https://stackoverflow.com/a/39383027/3560390

iOS 8 has changed notification registration in a non-backwards compatible way. While you need to support iOS 7 and 8 (and while apps built with the 8 SDK aren't accepted), you can check for the selectors you need and conditionally call them correctly for the running version.

Here's a category on UIApplication that will hide this logic behind a clean interface for you that will work in both Xcode 5 and Xcode 6.

Header:

//Call these from your application code for both iOS 7 and 8
//put this in the public header
@interface UIApplication (RemoteNotifications)

- (BOOL)pushNotificationsEnabled;
- (void)registerForPushNotifications;

@end

Implementation:

//these declarations are to quiet the compiler when using 7.x SDK
//put this interface in the implementation file of this category, so they are
//not visible to any other code.
@interface NSObject (IOS8)

- (BOOL)isRegisteredForRemoteNotifications;
- (void)registerForRemoteNotifications;

+ (id)settingsForTypes:(NSUInteger)types categories:(NSSet*)categories;
- (void)registerUserNotificationSettings:(id)settings;

@end

@implementation UIApplication (RemoteNotifications)

- (BOOL)pushNotificationsEnabled
{
    if ([self respondsToSelector:@selector(isRegisteredForRemoteNotifications)])
    {
        return [self isRegisteredForRemoteNotifications];
    }
    else
    {
        return ([self enabledRemoteNotificationTypes] & UIRemoteNotificationTypeAlert);
    }
}

- (void)registerForPushNotifications
{
    if ([self respondsToSelector:@selector(registerForRemoteNotifications)])
    {
        [self registerForRemoteNotifications];

        Class uiUserNotificationSettings = NSClassFromString(@"UIUserNotificationSettings");

        //If you want to add other capabilities than just banner alerts, you'll need to grab their declarations from the iOS 8 SDK and define them in the same way.
        NSUInteger UIUserNotificationTypeAlert   = 1 << 2;

        id settings = [uiUserNotificationSettings settingsForTypes:UIUserNotificationTypeAlert categories:[NSSet set]];            
        [self registerUserNotificationSettings:settings];

    }
    else
    {
        [self registerForRemoteNotificationTypes:UIRemoteNotificationTypeAlert];
    }
}

@end

As you described, you will need to use a different method based on different versions of iOS. If your team is using both Xcode 5 (which doesn't know about any iOS 8 selectors) and Xcode 6, then you will need to use conditional compiling as follows:

#if __IPHONE_OS_VERSION_MAX_ALLOWED >= 80000
if ([application respondsToSelector:@selector(registerUserNotificationSettings:)]) {
    // use registerUserNotificationSettings
} else {
    // use registerForRemoteNotificationTypes:
}
#else
// use registerForRemoteNotificationTypes:
#endif

If you are only using Xcode 6, you can stick with just this:

if ([application respondsToSelector:@selector(registerUserNotificationSettings:)]) {
    // use registerUserNotificationSettings
} else {
    // use registerForRemoteNotificationTypes:
}

The reason is here is that the way you get notification permissions has changed in iOS 8. A UserNotification is a message shown to the user, whether from remote or from local. You need to get permission to show one. This is described in the WWDC 2014 video "What's New in iOS Notifications"

Building on @Prasath's answer. This is how you do it in Swift:

if application.respondsToSelector("isRegisteredForRemoteNotifications")
{
    // iOS 8 Notifications
    application.registerUserNotificationSettings(UIUserNotificationSettings(forTypes: (.Badge | .Sound | .Alert), categories: nil));
    application.registerForRemoteNotifications()
}
else
{
    // iOS < 8 Notifications
    application.registerForRemoteNotificationTypes(.Badge | .Sound | .Alert)
}