First of all I want to make clear that most features aren't MVC-specific features. However, MVC does implement most of them out-of-the-box, while Web Forms needs some more installation and configuration work.

Front-end

Minification

There are some really neat features on the front-end part of MVC 4, first of all there's minification. Minification means that all spaces, enters and comments are removed from your CSS / Javascript files (including coffee, SASS and LESS), and that variable names are replaced with shorter variable names (such as a, b, c, etc.). This means that less data needs to be transferred to the visitors of your website, resulting in a faster page loading time, etc. Probably a feature that any front-end developer will love.

Bundling

Another cool feature that is often mentioned in one sentence with minification is bundling. Bundling means that you can have separate CSS files (e.g. one for your content, one reset style sheet, one for your layout) that are 'bundled' into one CSS file. ASP.NET does this by convention (but it's also configurable), for example: the reset.css will be placed in the bundle first, etc. This means that you only have one request instead of multiple requests, again resulting in a faster page load time.

Mobile web

Much has been done to improve the way MVC 4 behaves on mobile devices. There's now a mobile application project type that creates a nice lay-out that uses JQuery mobile to do all kinds of fancy stuff. MVC 4 also tries to render your lay-out in a mobile compatible way. This means that your elements are properly resized to fit inside the screen of mobile devices. But this is not the only feature, nor is it the most exiting feature. The most important mobile web feature (in my opinion) is the fact that you can now create device specific views. This allows you to create specific views for Windows Phone 7 devices, for Android devices, etc.

Project templates

For those who just want to make a quick prototype there are new project templates that look pretty fancy compared to the old project templates. Below is an overview of the new templates, the left template is the default template when you choose the 'internet application' project type, the second is the 'single page application' type and the third, obviously, the mobile type. The new project types also support AJAX login and OAuth.

Back-end

Web APIs

A very exiting new feature of ASP.NET is the introduction of Web APIs. This is another name for the new controller type, namely the ApiController. The ApiController makes creating an API much easier compared to WCF. Just like the default MVC controllers you can mark methods to be HttpPost methods, HttpGet methods, etc., but there are many new features to this.

The ApiController now allows users to perform queries against the API with OData if the ApiController method returns IQueryable<T>, it's possible to return specific HTTP codes to the consumer of the API, there's improved testability and IoC support, and more features that you will love.

Since the ASP.NET team and the WCF team have been merged, the new ASP.NET Web API wil replace some parts of WCF. This is a good things because the Web API is really easy (and flexible) to work with.

If you want to know more about ASP.NET's Web API I recommend Scott Guthrie's blog post about it.

Async

There was Async support in MVC 3. This meant that you need to have two methods: an Async method and a Completed method. MVC 4 removes the need for two methods and simplifies the way tasks are defined. Below are two examples:

The MVC 3 approach:

public void IndexAsync(string city) {
    AsyncManager.OutstandingOperations.Increment(2);
    NewsService newsService = new NewsService();
    newsService.GetHeadlinesCompleted += (sender, e) =>
    {
        AsyncManager.Parameters["headlines"] = e.Value;
        AsyncManager.OutstandingOperations.Decrement();
    };
    newsService.GetHeadlinesAsync();
     SportsService sportsService = new SportsService();
    sportsService.GetScoresCompleted += (sender, e) =>
    {
        AsyncManager.Parameters["scores"] = e.Value;
        AsyncManager.OutstandingOperations.Decrement();
    };
    sportsService.GetScoresAsync();
}

public ActionResult IndexCompleted(string[] headlines, string[] scores, string[] forecast) {
    return View("Common", new PortalViewModel  {
        NewsHeadlines = headlines,
        SportsScores = scores,
    });
}

The MVC 4 approach:

public async Task<ActionResult> Index(string city) {
    var newsService = new NewsService();
    var sportsService = new SportsService();    

    return View("Common",
        new PortalViewModel {
        NewsHeadlines = await newsService.GetHeadlinesAsync(),
        SportsScores = await sportsService.GetScoresAsync()
    });
}

As you can see the MVC 4 approach is much shorter and much easier, probably leading to more people using asynchronous methods. The code is still compiled into the same intermediate language, it's just syntactic sugar.

Real-time communication

There's also support for WebSockets and a new open source framework called SignalR that allows you to set up a real-time multi-user interactive website in a real easy manner. I highly recommend reading Scott Hanselman's blog post about SignalR and the official SignalR Github project.

Database migrations

The last feature that I wanted to mention is probably the coolest new feature. However, it's rather an Entity Framework feature than an ASP.NET feature. I'm talking about Entity Framework 4.3's new Database Migrations.

What it means is that Entity Framework can generate classes with Execute/Unexecute (actually they are called Up and Down, but I don't think those names really describe what they do), performing any database modifications that you've made. For example: let's say we have an entity called Person. If I wanted to add a property called 'Age' to Person entity, Entity Framework would generate a class for me with two methods: the Up method that adds the Age property to the Person table in the database (or whatever we've mapped the Person entity to) and the Down method that removes the Age property from the Person table. This allows us to rollback any changes, or easily perform updates on the database.

Entity Framework also allows us to generate SQL so we don't have to write change scripts manually any more. Automating the generation of change scripts can significantly reduce the time it takes to deploy your application, allowing the developers to focus on developing new features.