My problem regarding dragging clients (windows) across screens, I believe, is that I use a separate video card for each monitor. Maybe if I had multiple monitors connected to a single card, I could drag across them using Twinview, but currently I cannot. With Xinerama, I can drag across monitors, regardless what card the monitor(s) are connected to.

I try anew occasionally, to see if something has changed in the driver or the X server, but so far no luck.

Yes, OP is still around ), marvelling your prolific responses.
Thanks to you all!

It seems to me I might have caused some misconception using the word "desktop". I did NOT mean "virtual desktops" which most of the window managers support and between them windows can easily be moved by drag&drop. My scenario, however, is a combination of $DISPLAYs, one of them e.g. KDE at :0 and a vnc session running on :1. The "virtual desktop switcher" (kde4 plasmoid) handles virtual desktops, but not separate vnc displays, and the OP is not a Xinerama/TwinView thing.

Suppose you are working with thunderbird, lock your screen, move elsewhere, establish a ssh connection with a tunnel to your workstation where a vnc server is running, too, listening to some port at localhost only. You may now start a vnc session to your remote session and get an empty desktop (managed by the window manager you defined in .vnc/xstartup). Finally, you want to "pull" the window from one application :0 to :1, so to say.

Of course, when it comes to a mail client only, "killall thunderbird ; thunderbird" would be a simple solution, too. But what if the application you want to continue working with from the remote location (and maybe again locally, when you returned) could not be interrupted by kill without data loss?
The only workaround I know by now is working with a vncviewer even locally, and starting all applications you permanently need inside it.

But this is somewhat ill-favoured, there might be a smarter solution, too.

devdol: That is what I read in to your post. Did you see my earlier note on xpra ? I think this is what you need.

Would a working example of a program that does this help us figure out how to do it?

Gimp does.
On the menu, choose [view], then [move to screen], then choose the radio buttons for screen 0:0 or screen 0:1.

I have 4 monitors, 2 video cards each with 2 of the monitors hooked to them, and I can switch the window that you are editing the graphic in from one to the other by the menu (and back again).

I would be interested to hear if this option shows up when you only have 1 monitor (and one x Display).

Perhaps someone adept at reading C code could figure out the method that gimp is using and post directions so others (like me) can explore how to make more applications do this.