You can decide what emails you want to receive related to projects. You can choose to receive notifications for all activities, when you are mentioned, or for no activity at all. Apart from these, you can select events you want to be notified for apart from the activities.
Enabling email notifications
Click on Projects in the left panel.
Click on the project.
Click on the Settings.
Click on the My preferences tab.
Select the options for which you wish to receive notifications.
Click on Save changes.