Assuming you're on a computer (full version of R2R), hover over your name to get the menus and hit preferences. Under options, you should see "and receive email notifications of replies". Un-check that. You won't get emails anymore but you'll still see alerts in the upper right corner of the website.
If you ever want to be emailed for a watched thread, hit "watched thread" above the first post of the thread, and check to receive them for that thread.
Maybe an easier way, but that's how I found to do it. Hopefully this helps.