Drupal - How to allow for files of any extension to be uploaded?

You can use Allow all file extension Module

This module reverts Drupal 7's file upload widget to the Drupal 6 behavior, and trusts the site administrator to be smart enough to allow uploads with any file extension. It also lengthens the allowed file extensions box from 128 characters to 2048, allowing you to specify a larger number of extensions.

While I realize this is somewhat insecure and would have liked to add more functionality to this module, this isn't something I should have needed to do at all, and I don't have a whole lot of time to spend on it. If there are any bugs, I'll try to fix them, but beyond that, I won't be adding new features to it. If you would like add new features to this module, I would gladly accept a co-maintainer (or even transfer ownership to someone else).

Warning: The ability to leave the allowed file extensions box blank was removed for a reason. If you leave it blank and allow random users to upload files of any type, you'll have an insecure site. As such, you are strongly cautioned only to allow trusted users to do this.