This question explains how to create a new document in Photoshop CC with a transparent background.
What if you have already created a document (say with a white background) and now you want to change it?
NOTE: I'm not asking how to select a color with the magic wand and delete it from a layer.
Instead, I'm asking why the background itself used to be a layer in Photoshop (prior to CC) and you could delete it, leaving nothing behind the other layers.
You could also add a fill layer behind, of any color you wanted. I am still able to add a fill layer, but I can't figure out how to get rid of that white background.
Edit: When working with an image from the clipboard, the behavior I described works fine, just like it did in previous versions of Photoshop (select Background Layer in the Layers panel and delete it).
However, working with artboards (like what happens when you choose Web Large from the presets) seems to be different, and no Background Layer is apparent (yet the image itself still has a solid background):