How do I not receive an email whenever someone replies to a PM or sends me a private message?

[Ellie Williams]

I checked the settings page and I don't see an option for that.

 

[TheBrownster]

Under the settings page (or when you click your profile in the top right of any page), click on either Contact Details or Preferences.
In Contact Details, there is a box you can check if you would like to "Receive email when a new conversation message is received. Email notifications for new conversations, replies to existing conversations, and being added to an existing conversation."
In Preferences, you have another box for "and receive email notifications of replies" under the "Automatically watch threads that you create or when you reply..."

So to not receive emails for conversations or replies to a thread, just un-check those boxes and save the changes. :)