Roundcube webmail...
...is a browser-based multilingual IMAP client with an application-like user interface. It provides full functionality you expect from an e-mail client, including MIME support, address book, folder manipulation, message searching and spell checking.
This Quickstart has an accompanying blog post How To Setup Your Own Free Mail Server.
Create an OpenShift application with PHP, MySQL, and PHPMyAdmin cartridges
rhc app create roundcube php-5.3 mysql-5.1 phpmyadmin
cd roundcube
Pull the source code from this Quickstart
git pull -s recursive -X theirs git://github.com/openshift-quickstart/roundcube-openshift-quickstart.git
and import the database from a file in repository
php/SQL/mysql.initial.sql
Push the code back to OpenShift to deploy
git push origin master
This Quickstart is pre-configured to be used with the Mailgun service, however there are no blockers to use any other available service. To change this, edit the php/config/main.inc.php file accordingly.