UITabBar(Controller) - Get index of tapped?

The answer depends on whether or not the UITabBar is managed by a UITabBarController or not.

Case 1 - UITabBar is already handled by a UITabBarController

Implement the UITabBarControllerDelegate protocol. Specifically the tabBarContoller:didSelectViewController: method. Set an instance of your class that implements the protocol as the delegate of the UITabBarController.

- (void)tabBarController:(UITabBarController *)theTabBarController didSelectViewController:(UIViewController *)viewController {
    NSUInteger indexOfTab = [theTabBarController.viewControllers indexOfObject:viewController];
    NSLog(@"Tab index = %u (%u)", (int)indexOfTab);
}

In this case you have to be aware of the special situation where you have enough controllers in the tab controller to cause the "More" tab to be displayed. In that case you'll receive a call to the tabBarController:didSelectViewController: with a view controller that isn't in the list (it's an instance of an internal UIKit class UIMoreNavigationController). In that case the indexOfTab in my sample will be NSNotFound.

Case 2 - UITabBar is NOT already handled by a UITabBarController

Implement the UITabBarDelegate protocol. Specifically the tabBar:didSelectItem: method. Set an instance of your class that implements the protocol as the delegate of the UITabBar.

- (void)tabBar:(UITabBar *)theTabBar didSelectItem:(UITabBarItem *)item {
    NSUInteger indexOfTab = [[theTabBar items] indexOfObject:item];
    NSLog(@"Tab index = %u", (int)indexOfTab);
}

EDIT: Modified the method parameter variables to eliminate the OP's compilation warning about tabBarController being hidden.

SWIFT:

// somewhere inside your TabBarViewController
//...
override func tabBar(_ tabBar: UITabBar, didSelect item: UITabBarItem) {
    let indexOfTab = tabBar.items?.index(of: item)
    print("pressed tabBar: \(String(describing: indexOfTab))")
}

SWIFT 4:

I prefer

// somewhere inside your TabBarViewController
//...
func tabBarController(_ tabBarController: UITabBarController, 
                  shouldSelect viewController: UIViewController) -> Bool{
    let index = tabBarController.viewControllers?.index(of: viewController)
    return true// you decide
}