A lot of good answers here already. I'll give my recommendation which is not really different that what has been mentioned, but may give you a couple more things to consider.
First and foremost it would be helpful to develop a written document that discusses a file naming convention to be followed by all the staff. I have no idea what kind of work you do, but often files relate to certain projects or clients or cases, etc. If it is clients that you are concerned about, for example, it is very helpful to have a client name or client number in the file name. If dates are relevant and to be used in filenames, use a date code like YYMMDD. That way they will automatically sort in date order in the directories, which is helpful. That will not happen if you use MMDDYY or AUG06 for instance. You will have to work out what makes sense for your situation. It may be that you will have some files of each type and will segregate these into different folders.
Concerning a folder heirarchy, there should be a folder or drive for a given functional department, like Sales or Accounting, etc. Within that folder the second level should include a folder for each current employee. This is where each person will keep all the stuff they are responsible for and they can ortanize their folder as they see fit, but should follow the file naming convention. You will eventually have to set a size limit or guideline on these, so go ahead and do that now.
There should also be a departmental common folder at this second level and this is for things that concern the whole department. This departmental folder is where your organizational genius will be most needed. You will have to decide on whether you want everything pretty flat and let the search function take care of the rest. I highly recommend that solution. You may be surprised at how the default Windows search function will handle this. It may also be helpful to have a few folders at the 3rd level for obvious categories that you want to be browsable. There should be a folder with training materials that someone can read through, for instance. There might be a folder with staff meeting minutes. Whatever. It depends on what you have out there. Don't go nuts with a lot of folders and sub-folders to categorize everything. Search is your friend and faster than clicking throught endless levels of folders. Keep it simple. To paraphrase DA, use as many as you need but as few as you can get away with. With any complexity at all, it will simply not make sense to everyone and they will just be using the search function anyway.
Finally, at the second level alongside the current employee folders, you want a folder titled something like "former employees" and in there are the personal folders for people who have left. This keeps them from cluttering up the 2nd level and provides a place to park old stuff that didn't seem relevant enough to reassign when they left, but may be needed at some future date. You might also have a dumping ground in there for all the stuff that you think is outdated, but not related to a particular employee and something in there might be needed in the future.
Permissions can be set up so one employee can't change or delete stuff from another employee's folder, but can open, read and copy stuff as needed for cross-coverage of responsibilities. You should also have someone in charge of keeping things organized and adding new folders when someone is hired, etc. This person should have the permission level to make the necessary changes.