Ok, it's not really free, but it's damn cheap. Go to Go Daddy and sign up for a domain for less than $10(save even more by doing a google search for go daddy domains first and get their cheap coupon).
The domain is good for one year. You can be anything that is still available. You can be
yourname@yourdomain.com and that's a good thing. The problem is though that Go Daddy only gives you one email address for free and then it's only 25 MB. In this day and age that isn't enough.
Enter Google Apps for Domains at
http://www.google.com/a/ Google gives you as many 5 gb accounts as you want. It's connected to your domain. Say your domain is unvx.com. You can set it up so that you can use
teacher@unvx.com for your students to email you. You can use
name@unvx.com for your personal email. You can set up a catch all account as well, so when you're out, and someone wants your email, you can give them
anything@unvx.com and it will get to you.
Sure it isn't free, but it's damn close and it works great.