If you host upon a cPanel based server, you'll know about the two default webmail clients that are offered by default. Squirrel Mail and Horde. Both of these are capable email applications and have done well in offering webmail to a lot of people in the past.
Recently, a new player has come into the game, called RoundCube. It is still in beta status, but is extremely stable and a breeze to install on a cPanel server. It's a great looking piece of software and uses ajax where needed to make things easier. HostGeekZ have a very good guide available to use if you wish to try it out yourself.
As a bonus, if you use cPanel 11, it automatically detects the RoundCube installation, and makes the whole process even easier.
To install on my server with cPanel 11, I actually setup a new mysql user for RoundCube, rather than use the root user - and the instructions looked exactly like the link above, with an extra line after the database creation.
mysql -e "CREATE DATABASE roundcube;" -p
mysql -e "use roundcube; source SQL/mysql.initial.sql;" -p
// create a new user
mysql -e "GRANT ALL PRIVILEGES ON roundcube TO 'roundcube'@'localhost' IDENTIFIED BY 'SOMEPASSWORD';" -p




