Alerts:
Besides seeing all of your alerts in this tab you can also set your alert preferences (including how you get alerts)
Very important:
In the "Watched Threads" you can multi-check and then disable or enable e-mail notification:
Also, if you turn off the AutoWatch option, and you do want to watch a thread, there's a little linky at the top right of the thread to do so. Clicking on it pops this up:
So you can watch with or without e-mail notification, but it will still give you alerts and be in your "Watched Threads" list.