Your security department wants you to do this to make the server type harder to identify. This may lessen the barrage of automated hacking tools and make it more difficult for people to break into the server.

Within IIS, open the web site properties, then go to the HTTP Headers tab. Most of the X- headers can be found and removed here. This can be done for individual sites, or for the entire server (modify the properties for the Web Sites object in the tree).

For the Server header, on IIS6 you can use Microsoft's URLScan tool to remote that. Port 80 Software also makes a product called ServerMask that will take care of that, and a lot more, for you.

For IIS7 (and higher), you can use the URL Rewrite Module to rewrite the server header or blank it's value. In web.config (at a site or the server as a whole), add this content after the URL Rewrite Module has been installed:

<rewrite>    
  <outboundRules rewriteBeforeCache="true">
    <rule name="Remove Server header">
      <match serverVariable="RESPONSE_Server" pattern=".+" />
      <action type="Rewrite" value="" />
    </rule>
  </outboundRules>
</rewrite>

You can put a custom value into the rewrite action if you'd like. This sample sourced from this article which also has other great information.

For the MVC header, in Global.asax:

MvcHandler.DisableMvcResponseHeader = true;

Edited 11-12-2019 to update the IIS7 info since the TechNet blog link was no longer valid.

Correct way in new versions of nginx

Turn out my first answer to this question was correct at certain time, but it turned into another pitfall - to stay up to date please check Taxing rewrite pitfalls

I have been corrected by many SE users, so the credit goes to them, but more importantly, here is the correct code:

server {
       listen         80;
       server_name    my.domain.com;
       return         301 https://$server_name$request_uri;
}

server {
       listen         443 ssl;
       server_name    my.domain.com;
       # add Strict-Transport-Security to prevent man in the middle attacks
       add_header Strict-Transport-Security "max-age=31536000" always; 

       [....]
}