Moving files in Mac OS X is not as simple as it was in Mac OS 9 days, and is different from Windows as well.
Before deleting or moving any files you are uncertain of, be sure to make at least two backups of your critical data.
Files with a period as a prefix (i.e. .profile, and .DS_Store), should not be renamed or moved. These are files that are otherwise invisible in Mac OS X and help Mac OS X manage the system itself.
Don't delete or move mach files that appear when you double click the hard disk icon.
User folders must have their name maintained if you expect to be able to use X again. So if you first setup your Mac OS X account on setup as JSmith, don't rename or move the JSmith folder from the Users folder. We'll assume your user folder here on in your Users folder is your JSmith folder for example purposes only.
Unix defines directories and subdirectories by /es. So when I say /Users/JSmith/Documents/, that means you double click hard drive, double click Users, Double click JSmith, and double click Documents folder to get there from Mac OS 9. In Mac OS X View by columns allows you to navigate folders by single clicking on them, but they maintain the same hierarchy.
Don't delete or move files within System and Library folders appearing when you first double click your hard disk. Don't delete or move .App files in your Applications folder, these are Mac OS X native applications.
Don't delete or move files in your /Users/JSmith/Documents or /Users/JSmith/Library folder. Be aware that by default Mac OS X may set itself to put your iTunes music in /Users/JSmith/Music though that can be changed in the preferences, and iPhoto in /Users/JSmith/Pictures/
You can freely move the contents of these files and folders about, though not necessarily their subfolders (unless you created the folder):
/Applications Mac OS 9 - though I would test to make sure the application works after moving it. If it doesn't then move it back.
/Users/JSmith/ (except its default subfolders)
Observing all these rules will prevent headaches in the future.
If you find you must access any of the Mac OS X only folders while in 9 or running an application in Classic, return to X, and quit Classic and repair permissions (links to Apple knowledgebase explaining how to repair permissions)