Yes, right click the folder in question in the ZWC > share.
(See this blog post if you need an example:
/blog/archives/2007/08/shared-folders.html)
Mail, Address Books, Calendars, Tasks, Documents, and Briefcase folders can be shared.
Calendar, Documents, Briefcase all have REST HTML interfaces - for instance:
server.domain.com/zimbra/home/username/Calendar.html
Under construction:
Bug 26764 - Contacts - REST HTML interface Bug 26763 - Tasks - Rest HTML interface
Shares can also be configured several other ways, search the forums for CLI (zmmailbox) or soap.