From the Email Notifications (Home -> Members Area -> My Account -> Email Notifications) menu, enable / disable:

Messaging Notifications

If enabled, users will receive emails about the new messages received on the site.

Email Notifications

Select whether to receive email notifications from the website.

Note: Important emails regarding account status and sale / purchase notifications will still be sent.

Seller Notifications

Include closed, relisted, no sale, as well as approved and suspended listings notifications.

Offers Notifications

Include offers module related email notifications: new offer, counter offer, offer accepted, offer declined, offer withdrawn.