Go to User CP

Scroll down to Settings & Options, click Edit Options

Scroll down to Messaging & Notification section; look at the “Receive Email” box
Make sure the “Receive Email from Administrators” & “Receive Friendship Request Email” options are not checked

Scroll down to the “Default Thread Subscription Mode” box
Make sure the “Do not subscribe” option is selected

Scroll down to the “Private Messaging” box
Make sure the “Receive Email Notification of New Private Messages” option is not checked

Scroll down to the bottom of the page, and save changes.