"What's new" email updates: how do I change their frequency or turn them on or off?

By default, you get one email a week from the site with a list of new posts. You can change this at any time in your account settings.
 
Change what type of posts you get notified about: 
Go to the My account page. Select Notifications from the list of links across the top of the page. On the Notifications page, select Subscriptions. You will see a set of subscriptions to content like "private circle dialogs" and "member forum topic". You can set any of these to inactive, and that content type will no longer appear in the periodic email notification.
 
Change frequency of emails:
If you edit the individual subscription (see above), you can change the frequency from "weekly" to various other options (eg "daily"). You can inactivate it or turn it off too. If you inactivate all content types you will get no email at all.