For any deployable app (one explicitly checked and marked as deployable), we will send you a weekly status summary email. The content of the mail is identical to the contents of the Activity tab on the Account page. There are links in it to further details about each of the apps.
These will give you a 10,000 foot view of your apps on a regular basis without becoming too noisy.
You can disable these emails from your Account page on the Settings tab: