Free Software and Self-hosted File Managers (UPDATED)
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Sigma File Manager: An Open-source File Manager for Windows and Linux
"Sigma File Manager" is a free, open-source, quickly evolving, modern file manager (explorer / finder) app for Windows and Linux.
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Tiny File Manager: Self-hosted Free Web-based File Manager
TinyFileManager is a web-based PHP file manager that is a great solution for users who want a simple, fast, and compact file management system. Its small size makes it easy to download and install, and its single-file PHP format makes it easy to integrate into any folder on your server.
UPDATE
Another one:
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Rich Filemanager: Open-source File Manager for the Web
Rich Filemanager is an open-source file manager released under MIT license. Based on the @simogeo Filemanager,
* Drag-and-drop support * Clipboard feature: copy, cut, paste, clear * Selectable files & folders support (mouse dragging & Ctrl key) * Multiple actions support for selected files & folders: move, delete, download * Before and After callback functions for some