The user's home folder in OS X contains a number of default directories including the Documents, Downloads, Desktop, Library, Movies, Music, and Pictures folders. While these locations do not have to be used to store your files, even if you rarely use these folders to store your files we recommend you do not rename or remove them.
OS X should have default permissions settings on these folders that prevent them from being inadvertently renamed; however, if you migrate your system, restore it from backup, or purposefully change permissions, then this restriction might change and allow you to rename the folders.
Folders that the system uses
While most user folders are only storage locations, some are regularly accessed by running system and user processes that keep the account active and functioning, and are set up in such a way that if altered will likely result in undesired behavior. This specifically applies to the Desktop and Library folders, which if missing will prevent the user's desktop from containing and displaying files, and also prevent settings from being stored in the user's account.
To a lesser extent, the Public and Sites folders also are used by the system, since they are the default locations to share files between accounts and show sites via Web sharing. System settings that point to these files can be changed, but if they are not, then shared Web pages may suddenly go offline.
Folders that applications may use
Besides the Desktop folder, all other default folders in the user's account will likely be accessed by various applications the user uses. iTunes will store music in the music folder, and iPhoto will store libraries in the Pictures folder, and Final Cut and iMovie may regularly use the Movies directory. While you can set individual applications to use other locations, this may be difficult and tedious to do for all applications, and if you overlook one or two then they might not work properly if the folder is renamed.
If you do manage to rename one of these folders, while doing so usually will have no immediate repercussions, if you restart the system or try to invoke a change to the system, application settings, or your account settings after these folders have been renamed, then you might s run into problems.
Despite this, there sometimes are immediate problems that can happen if you change the name of these folders. For instance, if you run Parallels Desktop and have virtual machines open that are stored in their default location within the Documents folder, then changing the name of the Documents folder will result in the virtual machine shutting down and giving you an error that the virtual machine files are not available.
Overall while most people will not need to rename the default folders in their home directories, if done it may result in odd or broken system behavior that could be more of a headache to fix. Unless you have a specific reason for changing these folders, then its best to leave them as they are. If you have a specific need to change the default home directory setup, then it is best to do so in a fresh user account before you have applications and the system set up.
If you are able to rename the folders in your home directory (you can check this by highlighting one and pressing Enter to go to file rename mode), you might consider running a home folder permissions reset, which can be done with the Reset Password utility that's available in the OS X installation DVD. Boot to the DVD by holding the "C" key when starting up with the disc in the drive, select your language, and then select "Reset Password" from the Utilities menu. In this utility you can reset the home folder permissions, which should restore all default behavior and permissions settings to the default home directories.