I need two instances of AngularJS $http service or what?

1. Circular dependency problem.

So, why does the error appear? Here is a quick overview of the process:

1. $http service is requested.
2. $httpProvider is asked to construct it.
3. During construction you register interceptor, that requests $http service not existing yet.
4. You get "Circular dependency" error.

First solution.

Create your dependency using angular.injector(). Notice, that you will create another $http service, independent from your app.

$httpProvider.interceptors.push(function($q) {
    $injector = angular.injector();
    return {
        response: function(response) {
            $injector.invoke(function($http) {
                // This is the exterior $http service!
                // This interceptor will not affect it.
            });
        }
    };
});

Second solution (better).

Inject $injector in your interceptor and use it to retrieve dependencies after $http initialization, right at the time you need them. These dependencies are registered services of your app and will not be created anew!

$httpProvider.interceptors.push(function($q, $injector) {
    return {
        response: function(response) {
            $injector.invoke(function($http, someService) {
                // $http is already constructed at the time and you may
                // use it, just as any other service registered in your
                // app module and modules on which app depends on.
            });
        }
    };
});

2. Interception prevention problem.

If you use the second solution, there are actually two problems:

1. If you utilize $http service inside your interceptor, you may end up with infinite interceptions: you send request, interceptor catches it, sends another, catches another, send again, and so on.
2. Sometimes you want just prevent request from being intercepted.

The 'config' parameter of $http service is just an object. You may create a convention, providing custom parameters and recognizing them in your interceptors.

For example, let's add "nointercept" property to config and try duplicate every user request. This is a silly application, but useful example to understand the behavior:

$httpProvider.interceptors.push(function($q, $injector) {
    return {
        response: function(response) {
            if (response.config.nointercept) {
                return $q.when(response); // let it pass
            } else {
                var defer = $q.defer();
                $injector.invoke(function($http) {
                    // This modification prevents interception:
                    response.config.nointercept = true;
                    // Reuse modified config and send the same request again:
                    $http(response.config)
                        .then(function(resp) { defer.resolve(resp); },
                              function(resp) { defer.reject(resp); });
                });
                return defer.promise;
            }
        }
    };
});

Having the testing for property in interceptor, you may prevent the interception in controllers and services:

app.controller('myController', function($http) {
    // The second parameter is actually 'config', see API docs.
    // This query will not be duplicated by the interceptor.
    $http.get('/foo/bar', {nointercept: true})
        .success(function(data) {
            // ...
        });

});