We have the built-in ReopenTicket rule turned on, so that if someone other than the owner updates the ticket, it's reopened.  I had been thinking about how I could modify that to prevent out of office automatic replies from reopening the ticket, but this is even better, and easier, than that.  KISS, right?

This applies specifically to Office365, but I'd imagine other email systems have a similar feature.

Log into the mailbox you have set up to receive email for KACE Service Desk tickets, then go to Options > Inbox and Sweep Rules.  When you create a new rule, set the first box, "When the message arrives, and it matches all of these conditions" to It's > of the type... > Automatic Reply.  Then set the second box, "Do all of the following," to Move, Copy, or Delete > Move the Message to Folder... > and create a new folder in the Inbox where these can be stored.  That way, you can still go in and look at them to determine if they're actually valid requests which need to be handled, but because the type is Automatic Reply, they probably won't be.  Alternately, you could forward them to yourself to look at them.

You can do the same thing for emails of the type... > Non-Delivery Report, too.

And voila!  Now you no longer have out of office automatic replies or NDR emails cluttering up your Service Desk with unwanted comments, reopened tickets, and junk tickets.

I also looked in Outlook 2013, and in the Rules there, you can set the condition to "which is an automatic reply," so that would probably work in other environments, because it appears that is a server-side rule.  I don't see anything for NDR-type emails, though.

Hope this helps someone!