After completing this how-to you have the ability to set and disable reminders and alerts
Begin with the drop down arrow by your name in the page header and click My Settings
Then continue with expanding Calendar & Reminders in the side bar and clicking on Activity Reminders
Here you can update your activity reminders. Turn off trigger alerts, change default reminder times on tasks and events, and choose to disable reminder sounds.
To reduce the clutter in your inbox, we recommend un-selecting the check box "Email me when someone assigns me a task" unless you live out of your email and never log in to Salesforce.