Mark Smith

For those of you who still need this, I've found a work around that avoids using Zapier.  Hopefully you'll find this helpful.

You can configure Zendesk to send an email to a specific slack channel's email address.

First, you'll need to generate an email address for the slack channel you want notifications in.  You can find the instructions here

Next, in Zendesk, within the admin settings, under "Apps and integrations" select "Targets".  Create a target for new tickets, and a target for ticket updates. 

My configuration for the new tickets target:
Subject: A new ticket has been assigned to {{ticket.assignee.name}}
Email: The email address for your slack channel

My configuration for the Ticket Updates target:
Subject: Ticket Update: {{ticket.title}}
Email: The email address for your slack channel

You'll then need to create two new triggers.  One for new tickets, one for ticket updates.

My configuration for new tickets:
Conditions:
Ticket > Ticket | is | Created
Actions:
Notify by > Target |
Message:
Ticket URL: www.{{ticket.url}}
Requestor: {{ticket.requester.name}}
Assignee: {{ticket.assignee.name}}
Subject: {{ticket.title}}
Description: {{ticket.description}}

My configuration for ticket updates:
Conditions:
Ticket > Ticket | is | Updated
Ticket > Status | is not | Closed

Actions:
Notify by > Target |

Message:
Ticket URL: www.{{ticket.url}}
Requestor: {{ticket.requester.name}}
Ticket Status: {{ticket.status}}
Assignee: {{ticket.assignee.name}}
Subject: {{ticket.title}}
Comment: 
By: {{current_user.name}}
{{ticket.latest_public_comment_html}}

Virginia (Carrot Fertility) I'd like to know the answer to this one as well.