I thought to summarize my late experience with some mobile devices:

On Network Edition 6.0.6_GA_2332.RHEL4.NETWORK (soon 6.0.8)

iPod Touch/iPhone:
No problems here.
1. https://<yourserver>/zimbra/m to get the mobile web interface
or/and
2. setup an Exchange ActiveSync account. It works like a charm.

Android (tested with HTC Desire and Samsung Galaxy S)
HTC Desire
works with ActiveSync but doesn't send, so I setup an IMAP access and let ActiveSync take care of calendar and contacts

Samsung Galaxy S
On one ActiveSync doesn't sync contacts on another it worked right away.

Probably issues on implementation of ActiveSync on Android, whatever.
I solved it with TouchDown (Exchange for Android) by NitroDesk available from the Android Market. They specifically mention Zimbra on supported platforms.

Obviously on Android too https://<yourserver>/zimbra/m to get the mobile web interface saves your day , while you fiddle.

BlackBerry
Honestly I still not sure (I'm dum) what I need.
Network Edition ok
Zimbra Mobile enabled. Do I need a license?
Zimbra Connector for BlackBerry Enterprise Server Small Business Edition (ZCB)
And BlackBerry Enterprise Server Express

But do I still need a running copy of Exchange?