A function like: ng-click="alert('Clicked')"

Refer to previous answer, ng-click = "alert('Hello World!')" will work only if $scope points to window.alert i.e

$scope.alert = window.alert;

But even it creates eval problem so correct syntax must be:

HTML

<div ng-click = "alert('Hello World!')">Click me</div>

Controller

$scope.alert = function(arg){
    alert(arg);
}

As far as I know, ng-click works only within your $scope. So you would only be able to call functions, defined in your $scope itself. To use alert, you may try accessing the window element, just by using window.alert('Clicked').

EIDT: Thanks to Ibrahim. I forgot. You shouldn't be able to use window.alert, as far as you won't define:

$scope.alert = window.alert;

In this case, using alert('Clicked') in your ng-clicked directive should work. But at the end, this method would not solve your problem of not touching your controller.

As Neeraj mentioned, the accepted answer does not work. Add something like this to your controller to avoid an Illegal Invocation error:

$scope.alert = alert.bind(window);