There are several reasons a teacher may want to email students. Whenever I have students fill out a Google Form I like to ask for their email address so I can use a script such as flubaroo or valmerge to email the student feedback. I also will create a class newsletter that I email out occasionally with announcements and things. The problem is when a student does not have email.
Using your email, or create a new gmail account for students, you can assign students an email address without giving them an email address. If I were to create firstname.lastname@example.org I could assign students email by adding a plus and the students name within the email address. By simply appending +studentname within a gmail address the email is still valid.
Where Does the Email Go?
Unfortunately this does not fully solve the problem because these pseudo email addresses will simply forward to the original email. In this case email@example.com.
How Does This Help?
The email will show in gmail that it was sent to the modified email address. This allows the teacher to set up a filter to sort these emails into a particular folder. Either one per student or just one for all of the pseudo email addresses. Doing a search at the top of the gmail inbox for a particular pseudo email address will show the emails sent to that student. Knowing that that student does not have email, the teacher can print out the email for those kids.
This also helps for password recovery. If students are using Web 2.0 tools that ask them to provide an email address they can use their pseudo email address and the confirmation email will then go to the teacher who can confirm the account or help with password resets.