Our current project makes heavy use of drag + drop, using GWT and gwt-dnd you can make very cool stuff. Standards and works in IE6, Safari, Firefox, Opera, etc.
The question of how to transfer the file is a separate one, which I believe.
As for FTP support, I see that it is largely replaced by HTTP File Upload support.
In case you need more flexibility (progress bar, select multiple files), you can use the flash for this. You can use Javascript to interact with an invisible flash application that performs file transfer. Managing the loading of YUI files does this. You can see an example on the extended Flickr download page.
We have created a custom version for use with GWT applications. The same concept.
source share