The Zimbra Ajax web client is just one way to access the Zimbra Collaboration Suite (ZCS). I have to admit that it is the one I almost always use, because I am totally hooked on the conversations, searching, and the calendar features. I basically never throw any email away anymore since finding stuff is such a breeze. I also like the fact that I can access the ZCS from anywhere on any machine that runs a supported browser. However, all of the capability that is provided in the client is for the most part realized by the server. In addition the server supports IMAP/POP clients, as well as iCAL clients. Another cool and important fact is that all the APIs that the client uses are public SOAP APIs that are documented in the source code download (look for soap.txt & soap-calendar.txt in the docs directory).
I would really love to see other folks write clients against the ZCS server. These could be full blown collaboration clients, utility clients such as Mac OS X or Konfabulator Widgets, or integrations with existing web clients (i.e. using the ZCS as a data source).
As an example, Greg (one of the engineers at Zimbra) has developed a mobile flash client that runs on a PocketPC. It supports such features as conversations and autocomplete on compose. It also syncs calendar appointments from the ZCS calendar. Greg runs it on his PocketPC mobile phone and uses it all the time – As do several other folks at Zimbra.