And you don't set the `default_server` as this document suggest. `default_server` is a parameter to the `listen`-directive. The only reason the docs might work is because the first server-block defined, when no-one is defined as `default_server`, becomes the default server.
server {
listen 80 default_server;
return 444;
}
This will close the connection and log it internally, for any domain that isn't defined in Nginx.Edit: Shout-out to #nginx on FreeNode, where you'll always find someone to point you i the right directing or help you out.