I’m setting up a scenes with three emission planes as light sources in Cycles, but I only want one of them to cast shadow. Is it possible for a emission shader not to cast shadows?
Every shader can be set up in a way that there is no shadow.
Just go to the material settings and set the shadow mode to none.
I meant the emission doesn’t cast shadows on to objects like the settings in Physical Light 
So, I’m going over the possible settings in my mind that might “disable” shadow casting for emission shaders, but I’m not coming up with anything off the top of my head.
Can you tell us a bit more about what you are trying to achieve? I understand the idea of what you want to do, but I don’t understand exactly why you want to do it.
Im with @Hunkadoodle here, knowing what your goal is will help greatly. Obviously you dont want the shadows but knowing why could be of great help. Just coming from a more traditional stand point, for a production render you should be using render passes anyway and with the use of AOVs or render layers you could just not include the shadows on certain objects as you please, but this would of course require additional work in post. This additional work is pretty normal but it ultimately boils down to what work you want to do. There may still be a way to do it but given that this is standard practice anyway, passes and AOVs are probably the quickest solution.
yes in the object’s Viewport Display it would make sense to have a Cast Shadow option, we only have a Shadow option but it’s only for the object’s own shadow
I can’t disclose the project, but basically I’m creating gradient area lights using this trick. https://www.youtube.com/watch?v=94eYd_cldtw
It uses emission shader to simulate gradient area light in Cycles, but it can’t turn off shadow casting like light source can.
@ThorntonStrolia
The project has to be animated, so render pass processing is too time consuming.
render passes are completely intended for animation. They do not take any longer to render and all of the passes can be rendered to a single file if you use OpenEXR and then just turn off a layer after effects, or you can also do it in blenders compositor. Very quick and easy to setup. It will not take you any longer than looking for an answer here that will likely be a bit hacky. This is the intended purpose of passes and render layers.
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