Sharry allows to share files with others in a simple way. It is a self-hosted web application. The basic concept is: upload files and get a url back that can then be shared.
droppy is a self-hosted file storage server with a web interface and capabilities to edit files and view media directly in the browser. It is particularly well-suited to be run on low-end hardware like the Raspberry Pi.
FileShelter is a self-hosted software that allows you to easily share files over the Internet. Just upload a file and get an URL back!
miniserve is a small, self-contained cross-platform CLI tool that allows you to just grab the binary and serve some file(s) via HTTP. Sometimes this is just a more practical and quick way than doing things properly.
XBackBone is a simple, self-hosted, lightweight PHP backend for the instant sharing tool ShareX. It supports uploading and displaying images, GIF, video, code, formatted text, and file downloading and uploading. Also have a web UI with multi user management and past uploads history.