Roundcube Webmail is a mature and nice enough web email interface.

The installation process is pretty simple: you need to download the package, unpack it, copy it to the web folder, create a database, import the database schema and configure the app.

Create the database and the user:

mysql-p
create database roundcube;
grant all on roundcube.* to roundcube@localhost identified by '$ROUNDCUBE_PASSWORD';
flush privileges;

Download the package, unpack and copy it to the web folder:

wget http://sourceforge.net/projects/roundcubemail/files/roundcubemail/1.0.2/roundcubemail-1.0.2.tar.gz
tar xzvf roundcubemail-1.0.2.tar.gz
cp roundcubemail-1.0.2 /var/www/html/roundcube
cd /var/www/html/roundcube/config
cp config.inc.php.sample config.inc.php

Now edit config.inc.php

$config['db_dsnw'] = 'mysql://roundcube:$ROUNDCUBE_PASSWORD@localhost/roundcube';

and

cd ../SQL
mysql -u roundcube -p'$ROUNDCUBE_PASSWORD' roundcube < mysql.initial.sql

Now change directory to /var/www/html and create a simple index.php file that redirects users to /roundcube

<?php
  header('Location:roundcube');
?>