have a look at
http://www.roundcube.net/
There you will find a similiar working WEB-Client for IMAP, only.
But you will not have a calendar and these other "cool" functionalities like Zimbra has.
BTW: Zimbra looks great and might be one of the greatest Groupware i've ever seen in the web, BUT...BUT if the Zimbra-Team will NOT integrate a functionality to connect to normal IMAP Server like cyrus etc. there will NEVER be a critical mass of installations in world out there, because THIS is a widely wished requirement.
Sorry, but you can't force people to move their existing mail-system with millions and Gigabytes of mail in it to a new one. This migration is a major task, and as a Systemadministrator i will never do this, because there are soo many dependencies hanging on and finally it's very time intensive.
I really hope and wish, that there will a possibilty to do this in future releases.
Best regards,
Harry