SMS forwarded to email just shows up in SMS again

I don't know that you'll find a free one, because it costs money to maintain a server, the server in which you need to use with some software set up to communicate with the Apple Push Notification Service ("APNS").

We use Prowl (link goes to homepage, here is an iTunes App Store Link) at work in order to send Monitoring (NAGIOS) notifications to our phones. It's a $3 app, but it's also infinitely flexible.

It gives you an e-mail address you can use to just shoot notifications too, but it also offers an API you can use to do a lot of special things with.

More details if requested after you check out Zac's site. (Zac is the developer/maintainer/operator of Prowl app and it's associated server backend.)

You did not specify which inbox you checked, but if you use mail <your mac userid>, you can then read that mail by running the mail command without any arguments. I am not sure how useful this might be, but it does work.

man mail from a shell prompt will give you more background info into the mail command.

If you are looking to send email to an external (SMTP) mail server from a shell prompt (like the one in the Terminal window), you will need to use a message transfer agent or MTA. This is something far more useful, although it requires much more setup overhead.

Alternatively, you might be able to use Applescript and/or Automator to automate sending messages through Mail.app through a previously configured email account.