Zillow sends out several types of email alerts, therefore, there are a few places for unsubscribing.
Saved Searches: Click on "My Zillow" from the upper right hand corner. Then select "Saved Searches." On the following page, you can see the option to delete or edit your saved searches. You can also access your saved searches from the menu options at the top of the profile view. You can then update your subscription settings to "Never" in the drop down menu for each individual search. You can also chose to delete the search completely by clicking the "Delete" button.
Saved Homes: Select "Saved Homes" from the menu options at the top of your profile view. You will then see a list of the homes you have saved as your favorites. To remove a home from the listing, you'll want to un-check the heart icon on the property in question. Please note that in order to remove email alerts for Saved Homes, you'll need to remove the saved home from your list.
General emails and alerts: From your Profile view, navigate to the "Subscriptions" tab at the top of the page. You can then choose "on" or "off" for the desired subscriptions.