Tasks are the most important.
I think here if zimbra was able to provide at least the same functionality as M$ exchange/Outlook, that would be good.
BUT, why stop there. I have been waiting for tasks ever since we migrated over to zimbra. I have been playing around recently with a couple of different GTD (getting things done) tiddly wikis.
http://www.dcubed.ca/ http://simonbaird.com/monkeygtd/
The tiddly wiki uses javascript and CSS to create 'plugins'. The GTW plugins make it so that you can have different tags.