Execute action when back bar button of UINavigationController is pressed

One option would be implementing your own custom back button. You would need to add the following code to your viewDidLoad method:

- (void) viewDidLoad {
    [super viewDidLoad];
    self.navigationItem.hidesBackButton = YES;
    UIBarButtonItem *newBackButton = [[UIBarButtonItem alloc] initWithTitle:@"Back" style:UIBarButtonItemStyleBordered target:self action:@selector(back:)];
    self.navigationItem.leftBarButtonItem = newBackButton;
}

- (void) back:(UIBarButtonItem *)sender {
    // Perform your custom actions
    // ...
    // Go back to the previous ViewController
    [self.navigationController popViewControllerAnimated:YES];
}

UPDATE:

Here is the version for Swift:

    override func viewDidLoad {
        super.viewDidLoad()
        self.navigationItem.hidesBackButton = true
        let newBackButton = UIBarButtonItem(title: "Back", style: UIBarButtonItemStyle.Bordered, target: self, action: "back:")
        self.navigationItem.leftBarButtonItem = newBackButton
    }

    func back(sender: UIBarButtonItem) {
        // Perform your custom actions
        // ...
        // Go back to the previous ViewController
        self.navigationController?.popViewControllerAnimated(true)
    }

UPDATE 2:

Here is the version for Swift 3:

    override func viewDidLoad {
        super.viewDidLoad()
        self.navigationItem.hidesBackButton = true
        let newBackButton = UIBarButtonItem(title: "Back", style: UIBarButtonItemStyle.plain, target: self, action: #selector(YourViewController.back(sender:)))
        self.navigationItem.leftBarButtonItem = newBackButton
    }

    func back(sender: UIBarButtonItem) {
        // Perform your custom actions
        // ...
        // Go back to the previous ViewController
        _ = navigationController?.popViewController(animated: true)
    }

override func willMove(toParent parent: UIViewController?)
{
    super.willMove(toParent: parent)
    if parent == nil
    {
        print("This VC is 'will' be popped. i.e. the back button was pressed.")
    }
}

Replacing the button to a custom one as suggested on another answer is possibly not a great idea as you will lose the default behavior and style.

One other option you have is to implement the viewWillDisappear method on the View Controller and check for a property named isMovingFromParentViewController. If that property is true, it means the View Controller is disappearing because it's being removed (popped).

Should look something like:

override func viewWillDisappear(_ animated: Bool) {
    super.viewWillDisappear(animated)

    if self.isMovingFromParentViewController {
        // Your code...
    }
}

In swift 4.2

override func viewWillDisappear(_ animated: Bool) {
    super.viewWillDisappear(animated)

    if self.isMovingFromParent {
        // Your code...
    }
}