Tim Dwyer from the office next to mine has been working on code to move rectangles by the minimal amount enough that they no longer overlap.
Now he's spent a few days adding this to Inkscape (with a little help from me, njh & possibly Brisgeek): in the Align & Distribute dialog box near the existing Clump/Unclump buttons. (Unclump merely reduces overlap, whereas Remove Overlaps completely removes overlap.)
You can also think of it like the Distribute edge-to-edge buttons, except that it moves things only enough to ensure that they don't overlap; e.g. if applied to a set of objects that are roughly in a grid arrangement, then the new code probably does what the user wants (preserve the grid nature), whereas existing Distribute edge-to-edge would put the objects in a long diagonal line (unless the user does extra work, acting in small groups at a time).
This should be a significant addition to Inkscape's usability for diagramming.
Interface changes welcome; e.g. I wonder if it should be in the same box as Distribute; though having the separate box does make it clearer that the Hor/Vert Gap settings apply only to the Remove Overlap option.
pjrm.