Solution 1:

Apparently not using automatic injection. However, you can inject the injector and check for the service:

myApp.controller('MyController', [
    '$scope', '$injector', 'firstRequiredService', 'secondRequiredService', 
    function ($scope, $injector, firstRequiredService, secondRequiredService) {
        if ($injector.has('firstOptionalService')) {
            var firstOptionalService = $injector.get('firstOptionalService');
        }
    }
]);

Solution 2:

No, Angular does not yet support optional dependencies out of the box. You'd better put all your dependencies into a module and load it as one Javascript file. If you need another set of dependencies - consider creating another module in another JS and putting all common dependencies to common JS.

However, behavior you've described can be achieved with $injector service. You simply inject $injector instead of all your dependencies to a controller and pull dependencies from it manually, checking if they exist. That's it:

index.html:

<!DOCTYPE html>
<html data-ng-app="myApp">
  <head>
    <script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.0.7/angular.js"></script>
    <script src="app.js"></script>
    <script src="1.js"></script>
    <script src="2.js"></script>
    <title>1</title>
  </head>
  <body data-ng-controller="DemoController">
  </body>
</html>

app.js:

var myApp = angular.module('myApp', []);

myApp.service('commonService', function(){
    this.action = function(){
        console.log('Common service is loaded');
    }
});

myApp.controller('DemoController', ['$scope', '$injector', function($scope, $injector){
    var common;
    var first;
    var second;

    try{
        common = $injector.get('commonService');
        console.log('Injector has common service!');
    }catch(e){
        console.log('Injector does not have common service!');
    }
    try{
        first = $injector.get('firstService');
        console.log('Injector has first service!');
    }catch(e){
        console.log('Injector does not have first service!');
    }
    try{
        second = $injector.get('secondService');
        console.log('Injector has second service!');
    }catch(e){
        console.log('Injector does not have second service!');
    }

    if(common){
        common.action();
    }
    if(first){
        first.action();
    }
    if(second){
        second.action();
    }
}]);

1.js:

myApp.service('firstService', function(){
    this.action = function(){
        console.log('First service is loaded');
    }
});

2.js:

myApp.service('secondService', function(){
    this.action = function(){
        console.log('Second service is loaded');
    }
});

See it live in this plunk! Try to play with <script> tags and watch for console output.

P.S. And, as @Problematic said, you can use $injector.has(), starting from AngularJS 1.1.5.