Some Androids have a separate volume control for notifications. Settings -> Audio(Sound) -> Volume. (I think it may be in all but not exposed by the UI, so you may want to try widgetsoid or some other widget to expose the volume controls).
Failing that I think you can set the notification ringtone to "Silent".
Thanks, I think this did the trick. The main problem is the email program that's default on my Galaxy Note doesn't have a settings menu in the app, let alone one where I can turn off the notifications.
You might want to check out K9 mail. It's a fork of the vanilla Android mail app. It's been my experience that OEM modifications to the default apps break functionality like that more often than not.
Failing that I think you can set the notification ringtone to "Silent".