Yes, and the program is called Microsoft Windows. You can disable and re-enable USB storage access with a Registry tweak. And, because you can change the Registry only from inside an administrator-level account, only someone with such an account can do it.
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If you're comfortable working with Regedit, the key you want to go to is HKEY_LOCAL_MACHINE\SYSTEM\CurrentContro>Set\Services\USBSTOR. The value inside that key is Start. To disable USB storage, change Start's data to 4. To enable it again, change the data to 3.
But let me give you an easier way to change it. Copy and paste the code below into Notepad:
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\USBSTOR]"Start"=dword:00000004
[HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\USBSTOR\Enum]"Count"=dword:00000000"NextInstance"=dword:00000000
Now save the file, in a convenient location, and name it disableusb.reg. Make sure it's saved as a REG file, not a TXT file. You can tell by the icon.
Now repeat the process, with these two variations:
Launching disableusb.reg and confirming the change will--you guessed it--disable USB-connected storage. Note, however, that it won't affect storage already plugged in, but it will block any external drive that is plugged in after you make the change. Launching enableusb.reg will, of course, re-enable it.
How can you keep other people from launching enableusb.reg You need to have an administrator-level account to change the Registry. Assuming that only you have an administrator account, and that you haven't shared the password, only you will be able to make these changes.