I've noticed that all calendar notifications contain the following symbols (used as a kind of horizontal rule at the end of the email)
*~*~*~*~*~*~*~*~*~*
Just create a new folder in your mail and call it "notifications", then go to preferences, mail filters and create a mail filter that checks the body of the email for the symbols *~*~*~*~*~*~*~*~*~* (these symbols might be slightly different depending on your version of zimbra so just copy and paste from a notification message created by your version to be sure). In the actions panel set it to either file these messages into your new "notifications" folder, or just discard them completely. I would recommend simply filing them in your new folder as I'm not entirely sure if the system adds these symbols to any other notification emails... Still keeps the inbox nice and tidy though!
EDIT: Cancellation messages seem to make use of a slightly different string as a horizontal divider.... add the following rule to your calendar notification mail filter:
~ ~ ~ ~ ~ ~ ~ ~ ~
Also, in order for users to be able to see calendar events on which they are marked as 'attendees', the notification email must arrive in SOME shape or form, so if you discard the notification email via an email filter before it has even arrived, you will not see the corresponding calendar events if you are an attendee and not the organiser. You can get around this by using the 'notifications' folder technique mentioned above; keeps your inbox clear and you can delete the notifications regularly and easily
