Every mail server can be configured not to require authentication.
Or are you looking for a server that's running w/o authentication and which you can connect to? Those do not exist anymore - it's a basic spam prevention technique to require authentication for publicly accessible mail servers.
If you want you can have your own email server (Apache James). You this server to send emails. But beware mails which you send will mostly be going as spam, or will be stored in Bulk folder or even bounce back since receiving server might block non-domain incoming mails.