RoundCube is an excellent open source AJAX webmail client that makes older PHP webmail clients seem obsolete. It’s easy to set up provided you already have a working LAMP server (Linux, Apache, MySQL, and PHP). RoundCube does also work with PostgreSQL or SQLite, but that is not covered by this HowTo. For PostgreSQL or SQLite, refer to the README and INSTALL contained in the RoundCube tarball (sorry).
The aim of this HowTo is to make installing and configuring RoundCube a trivial 5 minute process.