Right now, there isn't a batch download option for files or images in the database. If you're looking for a quick way to save all files, you could try exporting the records.
Exporting a file field will provide you with the URL for the file's location in our server. You could add all those links to something like a Download Manager and have it manage all the downloads for you.
Another option would be to use the Image Sniffer tool, that comes with the Download Manager extension, while viewing a listing of your images, in order to automatically find all images on a page, and download them in a batch. Our testing indicates that files download into an HTML format so this tool may not work well for files.