This is intentional in 5.0.x - while 4.5.x let you have more than one session against the same server open in a single browser session, there's just too much that can go wrong. This is not specific for Zimbra but any session based application.
What you can do:
A) Use an alias domain mail.domain.com > webmail.domain.com and log one user into each. You can also put webmail.domain.com in the virtual hosts tab of the domain to make login smoother/avoid typing the full
username@domain.com if you have several domains.
Might not be scalable however, because if you're wanting 8 accounts open that'd be 8 webmailX.domains.com values to setup in DNS.
So if it was me, I would prefer to just make a wildcard-subdomain *.server.domain.com -> server.domain.com and have the users log in to username.server.domain.com.
B) Run multiple browsers (ie FF/Safari/IE)
C) Run multiple browser sessions of the same browser (search the web for more info).
For example-
Guide to running several independent instances of Firefox:
Running two Firefox profiles simultaneously - redemption in a blog
In short, close all your FF instances, run firefox -profilemanager, craete newProfileName, open firefox, then run firefox -P newProfileName -no-remote
You can use this extension to change the window title of the running instances:
https://addons.mozilla.org/en-US/firefox/addon/31
D) Want another easy browser to setup? You could use prism:
Mozilla Labs » Featured Projects
E) Use sharing! Plus, we now have shared mail folders in 5.0.x:
/blog/archives/2007/08/shared-folders.html
F) Share the send folder as well for keeping track of conversations, and it will be easy to reply as the user because of the built in on-behalf sending.
G) If you just need to be able to send as those users, you could setup a persona.
(You may need to set options like 'allow sending from any address' or spell them out specifically.)
H) If you just need to receive as these users and no one else does just do aliases
I) Forwarding if you want to keep an archive or something instead.
J) If it's just like one or 2 other accounts & you need full control over all these / own them anyways - try family mailboxes:
http://www.zimbra.com/forums/users/1...html#post67320 
(on-behalf takes care of the username when you send)