I'm running my Zimbra demo on a Mac Mini, 2 GB RAM, 1.83 GHz Intel Core Duo, Mac OS 10.4.11 (not Server).
Currently I have a production setup, using similar hardware, running Communigate and Meeting Maker for about 100 accounts each, and performance has been very good. I believe that Zimbra's demands are somewhat higher than either of those, though. Nevertheless our needs are modest compared to a lot of folks on this forum.
For remote access there's VNC (either the built-in host or Vine Server), Apple Remote Desktop (similar but seems to use some improved graphics compression to speed things up) and Timbuktu ($ but might be faster, YMMV). And ssh, of course.
If we go with Zimbra, I'd like to stay with Mac Mini but add an external Firewire RAID such as LaCie 2big or Drobo. I would also like to take advantage of the newer Mini models which support 4 GB RAM. However, until Zimbra NE is supported on Mac OS 10.5+, I'd have to make sure that the these can run 10.4. See
Bug 21441 – Requesting Apple-Server (10.5, leopard) support for ZCS and
Bug 32613 – OSX 10.5 DNS and other issues after system failure. With speed improvements due in OS X 10.6 (Snow Leopard), it would really be highly desirable for Zimbra to support it.
Another issue is
Bug 7039 – System kernel panic when zimbra server is mac dual core intel. It seems a shame to disable the second processor (although it's easy enough, using a free Apple download called CHUD Tools), and I haven't personally come across the bug whether running in single- or dual-processor.