Dependencies Between Modules - Controllers?

This tells AngularJS that all values, factories and services defined inside the myUtilModule should be available inside the myOtherModule module too. In other words, myOtherModule depends on myUtilModule.

var myUtilModule = angular.module("myUtilModule", []);

myUtilModule.value  ("myValue"  , "12345");


var myOtherModule = angular.module("myOtherModule", ['myUtilModule']);

myOtherModule.controller("MyController", function($scope, myValue) {

});

My question is: What if you define controllers inside myUtilModule and try to use them on myOtherModule. Is this possible?

Yes, controllers will also be available between modules, a pratical example could be as follows: 

angular.module('test.controllers').controller('HomeCtrl');

and then on your main module:

angular.module('test', [
    'test.controllers',
    'test.services',
    ...
];

This helps a lot on unit testing and reusability of packages.