From what I've seen of it an Angular application should have separate controllers for separate scopes. For instance, almost all applications have user data. You'll want to have this data attached to a user model, inside a user controller:
function UserCtrl ($scope) {
$scope.user = {
name: "bmorrow",
lastLogin: "4/16/2013"
};
}
And the template (our view) will be inside a specific portion of the applications structure. The right side of a navigation bar for example, or on a user details page. We establish where this portion is by assigning it a controller using ng-controller. This creates the scope of said controller and binds the corresponding models to it. The model (our data) is connected to the view (the HTML) via the controller.
Suppose the application has a page for the user's written articles. We can create another controller restricted only to the section of HTML that specifically holds the article content.
function ArticleCtrl ($scope) {
$scope.article = {
title: "Hello World",
body: "Lorem ipsum...."
};
}
In the trivial example above, combining both of the controllers won't do any harm. But once your application begins to grow, logically organizing your controllers/views according to the data it represents will make your code cleaner and easier to understand. Less unneeded complexity will make everything much easier on you. And using one controller for everything is an unneeded complexity.
You can see this illustrated in Basarat's answer as well. You don't necessarily need to use one controller per route, but doing so helps to logically structure the application.
So, to answer your question, you should usually have one controller per category of data. Users, Articles, Fruits, Vegetables, Transactions, and so on.
Read about Angular Controllers and the Model-View-Controller pattern for more information if you haven't already. I hope this helps.