the server responded with a status of 405 (Method Not Allowed)

try this

 [WebMethod]
 [ScriptMethod(UseHttpPost = true)]
 public List<Categories>  GetCategories()
 {
      //code
 }

or edit web.config

<system.web>
    ...
    <webServices>
        <protocols>
              <add name="HttpSoap"/> 
              <add name="HttpPost"/> --> 
              <add name="HttpGet"/>
              <add name="Documentation"/>
              <add name="HttpPostLocalhost"/>
        </protocols>
    </webServices>
    ...
</system.web>

Refer http://codeclimber.net.nz/archive/2006/12/22/How-to-enable-an-ASP.NET-WebService-to-listen-to-HTTP.aspx

make your content type as "application/json; charset=utf-8", as follows

$(document).ready(function() {
$.ajax({
type: "POST",
url: "RSSReader.asmx/GetRSSReader",
data: "{}",
contentType: "application/json; charset=utf-8",
dataType: "json",
success: function(msg) {
  // Hide the fake progress indicator graphic.
  $('#RSSContent').removeClass('loading');

  // Insert the returned HTML into the <div>.
  $('#RSSContent').html(msg.d);
 }
});
});

also refer link

I added a simple line on my friend's suggestion above the jquery ajax call

 jQuery.support.cors = true;

Now it is working fine :)

ONLY IN IE BROWSER

I would be happy to know if it can be solved using different way as it is not recommended.

Anyhow I asked this question again after many efforts and I got different error which was solved in this post here