Easy: Make a new folder named "Movies" where the old one was.
If memory serves, there's absolutely nothing magic about the Movies folder (or any of the other fancy-looking folders in your home directory) other than its location--the OS automatically gives it the fancy icon because of where it is, not what it is. The only "special" ones are the shared and drop box folders, which have special permissions to allow them to be used by other users of the machine.
Once you create your new 'Movies' folder in your Home folder, you may have to change permissions by highlighting the folder and pressing command + I. Go to the bottom of the dialogue box and make sure "Group" and "Others" are listed as 'No Access'.
Of course, this is only if you want your Movies folder to be inaccessible by other users, as it is in the default mac setup. You see, whenever you create a new folder in your home folder, os x automatically gives others on the computer read only permission to that folder. If you're afraid of prying eyes, I recommend always saving new stuff you make in the folders the mac made for you rather than just adding new folders to your home folder.