For example, I have two different objects. One cube and another- sphere. Can I somehow make cube change its shape identical to the sphere through animation? I mean I can do it manually with shape keys but is there some way to do it procedurally by just having start and final shapes even with different amount of vertices? The thing is I have two much more complex objects and transforming one into another is a hell of an ordeal.
Add a shape key (Key 1) and set its value to 1.000. Enter Edit Mode and use To Sphere tool (Shift+Alt+S,1). Then hit Ctrl+V-->Smooth Vertex. Hold Shift+R to repeat it (set smoothing value to 1.000 in a Tool Shelf) unless the vertices are relaxed. Then repeat the to sphere operation.