iPad 3 with USB hard drive
You can with the iPad Camera Connection Kit, but in a very limited manner. You can import photos or videos on an external drive to the Photos app, if you set up the file structure to emulate a USB-connected camera - I believe you need a folder in the root directory named DCIM with the photo and video files within named DCIM_1234.jpg (or .mp4, etc. as appropriate).

You may find this article useful: CNet: Secrets of the iPad Camera Connection Kit