There are two main settings related to email notifications about the submission of assignments (although related settings elsewhere can sometimes have an effect).
These options can be found in the Assignment Settings page.
To make a change in settings:
Go to your course page and either:
turn editing on for the course, then choose "edit settings" from the drop down next to the Assignment
click on the specific Assignment and then click on Edit Settings in the Assignment Administration block on the left
With the Assignment Settings page open, scroll down to the Notifications option and click to expand that section and change settings Yes/No as desired.
Also note that an individual student's preferences for receiving email notifications can not currently be changed, so they can not opt out of receiving notifications if faculty choose to have them sent.