Lets say that I have four layers using #ffffff. Now I want to know what my design looks like with #ffff00 instead. How can I do this without manually changing all four layers?
There's a few good ways to tag, filter and apply changes across your entire document. It's not the same as global colour swatches or CSS-like styles, but it's still very workable and fast.
Tag your layers
Tag your layers in a way that will allow you to filter them later. I've done this with layer colours below, but you could easily add tags to layer names or use some other method. It doesn't really matter how you do it, as long as you do things in a way that are filter-able at a later time.
Filter and Copy Shape Attributes
Now you can filter your entire document to only show layers with a certain tag. If you've changed one of the shape layers to the new colour, you'll now be able to right click and Copy Shape Attributes, then select the other layers and Paste Shape Attributes.
If your layers are bitmap layers, or you'd like to apply your colours and gradients, you can do so using layer styles (layer styles can be copied and pasted as well).
Please note that layer filtering is a Photoshop CS6 feature, and not available in earlier versions of Photoshop.