How to remove ‘create new post’ entry for a custom post type?

There are several ways (depending on what you’re trying to do):

If it’s about the “publish” button

You could…

1. …remove the capability from the targeted role with remove_cap()

2. …remove the publish button ¹⁾

   ^{1) see bottom of the answer by @toscho}

3. …or the whole meta box ²⁾

   remove_meta_box( 'submitdiv', 'custom_post_id', 'side' );
   

   ^{2) simplified version}

If it’s about the built in `post` post type

You could…

1. …simply hide the menu entry via css or js

2. …unset the menu entry with

   add_action( 'admin_menu', 'myprefix_adjust_the_wp_menu', 999 );
   function myprefix_adjust_the_wp_menu() {
     $page = remove_submenu_page( 'edit.php', 'post-new.php' );
     //or for custom post type 'myposttype'.
     //$page = remove_submenu_page( 'edit.php?post_type=myposttype', 'post-new.php?post_type=myposttype' );
   }
   

3. …prevent saving at all with the per_save_post hook and $_GET['action']

4. …do a redirect when the post-new.php is load