Remove notifications for one specific email account on Mountain Lion's Mac Mail
Actually, it is possible - here's how:


Create a smart mailbox ( Menubar > Mailbox > New Smart Mailbox ) which shows the content of all the mailboxes that you would like to get notifications for, and give it a nice name (for example, 'Notifications'). In my case the only rule in this mailbox is a 'Message is in Mailbox' - but you can be creative!





Go to the General section in Mail preferences ( Menubar > Mail > Preferences ) or press ⌘ + ,. About half way down you'll see the setting 'New message notifications' - open the drop-down and select the smart mailbox created under step #1.