This is a "web-application design" question, not an html question.
So redirect me to the right group, if appropriate.

If you wanted to build a drag-and-drop html and forms editor--as
a desktop application--you (the software designer) would have
many language/library choices. But what if you wanted this to be
a browser-based web application? What drag-and-drop options
are there

I've worked some with Google's GWT libraries, where you write Java
code that gets compiled into Javascript, that makes remote method
calls to the server, using a Java format that looks a lot like Java
RMI.
Does GWT support Java's drag-and-drop libraries?

Would flash be a reasonable choice?

Are there existing Ajax libraries that support drag-and-drop events,
that can be attached to server callbacks?

If a web-based drag-and-drop editor was you goal--for what ever
purpose--
what would be the right road to go down (when you get to a fork
in the road, take it?)