I'm new to Blender and I'm trying to bake the shadows of an object. But each time I do, the bake turns out all black. Every other baking option (Ambient Occlusion, Combined, Normal, etc.) works fine.
The limitation of baking Shadows is the same currently as with rendering a Shadow Pass in Cycles. The Shadow Pass will only receive its contribution from Blender Lamps. It doesn't work currently with mesh lights, which you are using to emit light into your scene. Try adding a sunlamp just for testing purposes and check if the Shadow Pass then bakes as expected. In my tests here it did. If that works, replacing mesh lights with area lights might be the way to go for you.
Here's a potential workaround, based on what @aliasguru said about mesh lights not baking in Cycles:
Save a copy of your .blend.
Make the diffuse material of the bake object white.
Do a diffuse bake.
Use the result as a shadow bake.