Well it depends on your design goals. Let's say you have a rail system on your beam to move your load. How much deformation can you take before rolling is affected? What if you have electrical or pneumatic lines, gears, piston-cylinder arrangements, etc. along your beam, how will the deformation affects those components? It is like the trailer I showed you: How flat do you want the bed to be under load?
If the stresses are OK, there is really no good or bad displacements. Of course, you have to make sure that the displacement will not somehow create some new conditions that will change your loading (like hitting another component, for example).
Displacement might be a good or bad thing in a dynamic case too. Displacement means low stiffness, which means better absorption of shocks. But if the stiffness causes the structure to be in synch with its natural frequency, it could cause a lot of troubles.