-didSelectRowAtIndexPath: not being called

Your problem is case-sensitivity. Your code:

- (void)tableVIew:(UITableView *)tableView didSelectRowAtIndexPath: (NSIndexPath *)indexPath {

should be

- (void)tableView:(UITableView *)tableView didSelectRowAtIndexPath: (NSIndexPath *)indexPath {

I have found the answer. I had a UITapGestureRecognizer set for myTableView's superView. This overrode the selection call. Credit to whoever suggested that that might be it. Your answer was deleted before I could mark it correct.

Set the cancelsTouchesInView property to NO on the gesture recogniser to allow the table view to intercept the event.

Updated for Swift 3:

if you are used UITapGestureRecognizer in your code :- # Swift 3 use below lines of code:

extension YourViewController{
    func hideKeyboardWhenTappedAround() {
        let tap: UITapGestureRecognizer = UITapGestureRecognizer(target: self, action: #selector(YourViewController.dismissKeyboard))
        view.addGestureRecognizer(tap)
        tap.cancelsTouchesInView = false
    }

    func dismissKeyboard() {
        view.endEditing(true)
    }
}

How to called:- In ViewDidLoad()

self.hideKeyboardWhenTappedAround()

Have you defined instance variable for tableview with same name. If not then might be this can be the issue-

_myTableView.delegate = self;
_myTableView.datasource = self;

Or-

self.myTableView.delegate = self;
self.myTableView.datasource = self;