SwingWT offers many benefits:
More responsive GUIs and faster startup times
Less RAM usage for applications
Many developers prefer the Swing API
Existing Swing applications don't need to be recoded
Mature Swing UI designers can be used
Developers deploying to *nix/Win32 can compile natively with GCJ and the applications can be distributed without a VM. Linux distribution makers could package many existing Java/Swing applications that previously could not be distributed in workable state.
SWT components can be directly accessed through the API, allowing mix and match (make eclipse plugins with Swing!)
All platform benefits such as font sub-pixel decimation for LCD monitors (unavailable in Swing)
Use Swing on mobile devices!
The best of both worlds! New Swing components for JClosableTabbedPane, JCoolBar, JTaskTrayItem..
Insulation from changes to the SWT APIs
Insulation from differences between SWT platforms
Documentation
See the SwingWT Javadocs.
Feedback
I always like to hear feedback! Let me know what I'm doing right/wrong! Contact me here, you could join the mailling list. You could also donate something if you like and use SwingWT
Download
Download the source and binaries for the latest version of SwingWT here. SwingWT is dual-licenced under the terms of the Common Public Licence and the GNU Lesser General Public Licence (LGPL).