This article lists some alternatives to DreamHost's Webmail service.
Hosting with non-DreamHost mail
The Custom MX page has options to use Google Apps / Gmail or any other mail provider for your domain.
Using Gmail as a Webmail client
Installing your own Webmail client
It is possible to set up any web-based IMAP mail client as a replacement for the default Webmail interface. You can disable DreamHost's Webmail for a domain using the Webmail page. This will free up the Webmail subdomain for you to use with your own Webmail client.
You can install your own version of alternative applications such as SquirrelMail or Roundcube. There are other popular Webmail clients including Horde and Open Webmail.