How To Hide From BuiltWith?

From their suggestion page:

The technology has to be discoverable in either the page body, cookies or server headers.

In theory, this could also involve things like testing known locations, such as http://example.com/wp-admin/

Most applications let you hide various bits of such identifying information, but on the whole: get over it if not. Hiding what apps you use isn't going to make nearly as much difference as keeping them up to date and secure.

If you are using Apache, you can turn off its signature as detailed on this page: http://www.shanison.com/2012/07/05/unset-apache-response-header-protect-your-server-information/

Sites can tell what server software you are running through the Server and X-Powered-By headers, as well as by message placed on error pages by the server. Use the following directives in httpd.conf to turn them off:

ServerSignature Off
ServerTokens Prod
Header unset Server  
Header unset X-Powered-By

For the Header command to be used, you'll need to be running Apache 2.x or higher with mod_headers enabled:

LoadModule headers_module modules/mod_headers.so  

Builtwith.com provide a link to block your site from their lookup service:

http://builtwith.com/removals

As others have pointed out, this does not prevent other services or methods of finding out what tech your site uses, but this essentially answers your main question.