Unlike Mac OS 9, Mac OS X has numerous files which should not be touched by someone unless there is a problem with the computer and it isn't behaving correctly. Among these files that should not be moved or renamed are:
the Applications folder *
The Library folders and files inside Library folders
The Documents folder, and files inside Documents folders that you did not manually save or copy there.
The Users -> yourname folders and the Users folder itself.
The System folders*, files inside System folders.
the folders and the files inside Picture, Music, and Movie folders if you use iPhoto, iTunes, and iMovie respectively. These are the storage locations for their documents.
Applications written by Apple inside the Applications folder. You can double click them, create aliases of them, but moving them may prevent them from being updated. The same is true with applications by other vendors unless the installer gives you the option to move the application anywhere you want.
You will want to backup these files and folders every so frequently as there are changes, but you don't want to move or rename them.
You can create folders and documents within the Users -> yourname folder for your own storage, as well as the Users -> Documents folder as long as you give them unique names that you'll know they are folders and documents of your own creation. The is with making aliases of applications, as you can make aliases and folders of aliases so you can more easily access those files.
If your machine is misbehaving, or you moved, deleted, or renamed these folders by mistake, please ask on the board here how to restore them properly.
* The Applications Mac OS 9 folder, and the System Folder with the Control Panels folder inside of it belong to Mac OS 9 and Classic environment. If you find you need to remove these, check on the board what's the current best way to remove them.