If you want to use Redmine with Zimbra/Postfix to send email notifications, for example, you can do so. Let's say you are using Ubuntu. You would run this command:
 
zcat /usr/share/doc/redmine/examples/configuration.yml.example.gz > /etc/redmine/default/configuration.yml

Then edit /etc/redmine/default/configuration.yml and find the uncommented smtp configuration. Change it as follows:

default:
email_delivery:
delivery_method: :smtp
smtp_settings:
address: your_zimbra_host
port: 25
domain: your_mail_domain

After this, restart Apache (or whatever you're using to serve Redmine) and go to the Redmine web interface, Administration > Settings > Email notifications and change them to fit your needs.

This configuration should fit any SMTP server, being it Postfix, Zimbra, or Sendmail.