Google Docs has a flexible system of organizing documents. While initially Google Docs used a labeling system similar to the one from Gmail, the current version combines the benefits of labels with the simplicity of folders. The interface names them folders, but they're actually hierarchical labels.
You can add a document to multiple folders without creating copies. Just go to "all items" and drag the document to more than one folder. Since the sidebar doesn't show subfolders, you can't drag the document to a subfolder.
What if you want to remove one of the labels? There's no interface option for this, but you can use this workaround: click on the label you want to remove in the sidebar and drag the document to one of the other labels. To remove all the labels, drag the document to "Items not in folders".
Google's hybrid between folders and labels still needs some improvement: subfolders are not displayed in the sidebar, you can't add multiple labels in a single step and it's not obvious that folders are actually labels.