A while back I wrote an article about an open source alternative to Exchange called Zimbra. Zimbra was acquired by Yahoo recently and it appears that Yahoo is continuing to develop this product. Yahoo released the Yahoo Zimbra Desktop today as a free download. (Be aware, it's rather large.)
This email/productivity software works in the off-line mode and also has available options for word processing, spreadsheets, task management, and more. The desktop runs as a stand-alone application and uses JAVA to store data locally. Google has been working on something similar, built on the open source “Gears” project, but has yet to release anything.
The Zimbra Desktop does not run in a browser, it's more like Outlook. A nice feature is that it functions so much like Outlook that even the keyboard shortcuts you're used to using with Outlook will work within the Zimbra application. A few “gotchas” remain though, most notably that it doesn't sync with your contacts/calendar (you have to do a manual export/import) and the IMAP folder sync seems to be a bit funky.
All in all, it's not a bad first attempt. Take a look at it if you're contemplating an alternative to Outlook. Just keep your fingers crossed that a Microsoft Yahoo buyout doesn't happen; the Zimbra suite is a major competitor to Exchange and we know what would happen to Zimbra if a deal goes through.