and a sequence of some kind of topographic grayscale images or lets call it a "height-map" (applied as the bumpmapping sequence) should produce the effect seen in 'X-men'. You know, that shot with lots of tiny blocks shaping a three-dimensional figure by movin up/downwards...
Without extensive script or plugin programming!
Ok here's a few possible ideas.. all more or less the same answer just different ways of reaching it.
First I will say bump maps are unlikley to get what you are looking for and the same for displacement maps (like you said) so you really do need to work with the actual geometry.
My first suggestion would be to build your map as you would with a set of wooden blocks buy using cubes with what ever shaders or textures you want on them.. once built you can save a key on the objects there for their translations. You will only need the blocks seen so don't go building the ones that would be underneath others. then what you do is go to your first frame or what ever frame it is that it's flat.. and reset their translations to 0 for every cube then save annother key.. this will have them build the structure gradually which may not be what you want..
The other idea is to build in levels. start at 0 grab the ones you want tanslate them up one step save key grab more trasnlate all up one more step etc untill done this will give you more of a contraolled step by step look.
The other idea is (and this could be better if you have multiple locations.. is to take a cube and subdevide the surface into sections (the amount that would represent the resolution of the 3D screen you are making) then duplicate the poly's on the surface as seperates.. not on a whole. Then you can grab them and translate in y to the hight you want and when done with one structure save a shape key.. then the next and so one.. you can mix between shapes or go from one to the other at whim in the Fcurver editor.
All of these are a lot of work but no more than you would have to do otherwise.. the other options are most certainly going to be expressions or plugins..
Hope one of these helps give you some ideas of how to tackle it..