How can I turn off the email notifications?

E-mail Notifications & SMTP
It can be done globally by an Administrator - for all projects - as follows:

1. Login as 'Administrator';
2. Go to: Administrator user menu -> Settings -> Notifications;
3. Remove the tick on "Enable notification system" option.

Notifications can also be disabled for a specific project - by a 'Project manager'.
To do that, open a project details page, click 'Notifications' button, then click on 'Disable' link for the 'Common notification rule' and custom rules if any. Close the window at the end.

Note that every project can contain a list of users who won't receive emails from that project, it is setup by the "Never notify persons from list below" option (see the above screenshot).

A user can override global notification settings and disable receiving personal emails on the My Options page:

Or disable personal notifications for specific projects: