Kontact can be configured to connect to the Zimbra server via IMAP to access all your e-mail.

Kontact can be configured to connect to the Zimbra server via LDAP to access the global addressbook. Haven't yet found a way to access the personal addressbook, though.

Kontact can also be configured to access the Zimbra server via HTTP to retrieve the .ics file for a personal calendar. The method to do so is:

To have read-write access to a Zimbra calendar, you need to login to the
web client, create a new calendar, give it a name (without spaces to make
the URL look nice), and share it as a public calendar (view only). Once
that is done:
- open the calendar section of Kontact
- click the Add button under Calendar resources on the left
- select "Calendar in Remote File" option
- give is a name like "Zimbra Calendar"
- enter the Download URL:
http://zimbra.sd73.bc.ca/home/<username>/<calendar name>/
- enter the Upload URL:
http://zimbra.sd73.bc.ca/home/<username>/<calendar name>/
- set the "Automatic Reload" options
- click OK

You now have the ability to create entries in the web client and view them
in Kontact, and to create entries in Kontact and view them in the web

Be sure to set your timezone correctly (use Settings -> Configure Calendar and not Settings -> Configure Kontact).

Access to the briefcase and other files is via the webdav:/ KIO-Slave.

No connectors needed, and (just about) all your data is accessible.