How to set a mesh to be shadowless?

Two questions actually. I have a mesh that I want to have a dim shadow and another mesh to have no shadow. I know I have made a mesh with no shadow before but when I tried to make it happen again it didn’t work. So… can any one out there tell me how to make a shadowless mesh? Second question: I fell like this is a very basic question but how do I make a mesh have a very dim shadow? Keep in mind that both theses objects (shadowless object and object with the dim shadow.) will be in the same scene. Thanks for your answer.

It does depend upon which render engine you use, but here is a setup for Blender internal.
Basically you need a different material for each shadow case. Shadow is controlled by the material that the shadow falls upon, not the casting object. To control the intensity of the shadow just adjust the Transparency of the shadow catching plane.


26_shadow_example.blend (489 KB)

Your .blend has the two objects on separate planes. In my scene the objects are floating and sitting above one plane. If I applied the Z transparency to the plane then wouldn’t all objects on the plane have some to no shadow depending on what the transparency is? I wanted to have both objects on one plane.
I have uploaded an image of the scene and the shadow that has been circled is the shadow i don’t want, all the other shadows I want. The object that is invisible is casting a shadow and i don’t want it to, it is supposed to appear and disappear. Also, what do you think of the scene? There is probably 100 things you could tell me i’m doing wrong. Could you tell me what i could do better on? Don’t hold back.