Zimbra announced at Web 2.0 yesterday that they were going to add an offline mode to their AJAX office suite. Any actions done offline will be stored in the local cache until you are back online. This will work for their email, calendaring, contacts, and documents offerings. You can learn more on their blog and on their product page.
Web apps have longed needed the ability to sync offline. Productivity apps in particular are in dire need for this. One of the reasons that I do not use Google Calendar is that I have no (easy) way to sync it from iCal, my offline calendar app. If there was an offline app that would sync to Google calendar then I would even consider switching just for that feature. Scrybe (reviewed by TechCrunch and eHub recently made waves for making offline syncing apart of their initial product offering.
This trend will continue as companies realize that this is a necessary feature to be competitive in the productivity market. Firefox already supplies mozStorage for this use and it will be updated with ease of development in mind for Firefox 3.0 and renamed to Unified Storage.