You can see this post first ASP.NET MVC Render Partial View to String. This post shows how to implement a RenderPartialViewToString method. To avoid the need of a parent class for each controller that implements this (helper) method I decided to use the following extension methods:

/// <summary>
/// Controller extension class that adds controller methods
/// to render a partial view and return the result as string.
///
/// Based on http://craftycodeblog.com/2010/05/15/asp-net-mvc-render-partial
view-to-string/
/// </summary>
public static class ControllerExtension
{ 

  /// <summary>
  /// Renders a (partial) view to string.
  /// </summary>
  /// <param name="controller">Controller to extend</param>
  /// <param name="viewName">(Partial) view to render</param>
  /// <returns>Rendered (partial) view as string</returns>
  public static string RenderPartialViewToString(this Controller controller, string viewName)
  {
    return controller.RenderPartialViewToString(viewName, null);
  } 

  /// <summary>
  /// Renders a (partial) view to string.
  /// </summary>
  /// <param name="controller">Controller to extend</param>
  /// <param name="viewName">(Partial) view to render</param>
  /// <param name="model">Model</param>
  /// <returns>Rendered (partial) view as string</returns>
  public static string RenderPartialViewToString(this Controller controller, string viewName, object model)
  {
    if (string.IsNullOrEmpty(viewName))
      viewName = controller.ControllerContext.RouteData.GetRequiredString("action"); 

      controller.ViewData.Model = model; 

      using (var sw = new StringWriter())
      {
        var viewResult = ViewEngines.Engines.FindPartialView(controller.ControllerContext, viewName);
        var viewContext = new ViewContext(controller.ControllerContext, viewResult.View, controller.ViewData, controller.TempData, sw);
        viewResult.View.Render(viewContext, sw); 

        return sw.GetStringBuilder().ToString();
      }
    } 

}

Using this extension methods my controller actions handling the AJAX requests look like this:

[HttpPost]
public ActionResult Update(int id, Model model)
{
  if (ModelState.IsValid)
  {
    // Update the database
    [...] 

    // Partial/FormUpdated contains a success message
    return Json(new Object[] { true, this.RenderPartialViewToString("Partial/FormUpdated", model) });
  } 

  // Partial/Form contains the form with all server-side validation errors
  return Json(new Object[] { false, this.RenderPartialViewToString("Partial/Form", model) });
}