EDIT : 31/10/2017

The same code/approach will work for Asp.Net Core 2.0 as well. The major difference is, In asp.net core, both web api controllers and Mvc controllers are merged together to single controller model. So your return type might be IActionResult or one of it's implementation (Ex :OkObjectResult)

Use

contentType:"application/json"

You need to use JSON.stringify method to convert it to JSON string when you send it,

And the model binder will bind the json data to your class object.

The below code will work fine (tested)

$(function () {
    var customer = {contact_name :"Scott",company_name:"HP"};
    $.ajax({
        type: "POST",
        data :JSON.stringify(customer),
        url: "api/Customer",
        contentType: "application/json"
    });
});

Result

contentType property tells the server that we are sending the data in JSON format. Since we sent a JSON data structure,model binding will happen properly.

If you inspect the ajax request's headers, you can see that the Content-Type value is set as application/json.

If you do not specify contentType explicitly, It will use the default content type which is application/x-www-form-urlencoded;

Edit on Nov 2015 to address other possible issues raised in comments

Posting a complex object

Let's say you have a complex view model class as your web api action method parameter like this

public class CreateUserViewModel
{
   public int Id {set;get;}
   public string Name {set;get;}  
   public List<TagViewModel> Tags {set;get;}
}
public class TagViewModel
{
  public int Id {set;get;}
  public string Code {set;get;}
}

and your web api end point is like

public class ProductController : Controller
{
    [HttpPost]
    public CreateUserViewModel Save([FromBody] CreateUserViewModel m)
    {
        // I am just returning the posted model as it is. 
        // You may do other stuff and return different response.
        // Ex : missileService.LaunchMissile(m);
        return m;
    }
}

At the time of this writing, ASP.NET MVC 6 is the latest stable version and in MVC6, Both Web api controllers and MVC controllers are inheriting from Microsoft.AspNet.Mvc.Controller base class.

To send data to the method from client side, the below code should work fine

//Build an object which matches the structure of our view model class
var model = {
    Name: "Shyju",
    Id: 123,
    Tags: [{ Id: 12, Code: "C" }, { Id: 33, Code: "Swift" }]
};

$.ajax({
    type: "POST",
    data: JSON.stringify(model),
    url: "../product/save",
    contentType: "application/json"
}).done(function(res) {       
    console.log('res', res);
    // Do something with the result :)
});