In ASP.NET MVC the convention is that a controller action method should return an ActionResult (or a type derived from ActionResult).
However, you can write a public method that returns pretty much anything and if that method is called (from a browser) the framework will package the return value up as a ContentResult and the browser receives a page of plain text.
This is all very interesting - but would you ever want to do this?
When you want to render something directly from your controller? e.g. using Response.Write(...); (or using other Response methods).
Not returning anything from an action method is essentially not responding to the client's HTTP request with a response.
An empty request might make sense in some cases (HTTP status being enough of a reply), but all web application patterns return something more than this (including, if I understand it correctly, REST: the new state of the entity).