you can grab a window with your mouse (left click) on its upper panel hold it, so that you can drag it around your desktop. To drag it to the next desktop just hold it + CTRL+1 or 2,3,4 (depending on your set desktops).
Ah, missed the most important bit in my comment: I could do this in Linux without the mouse, which is the behavior I want to replicate in OS X if possible.
