Peer-to-peer file transfers in your browser Cooked up by Alex Kern & Neeraj Baid while eating Sliver @ UC Berkeley.
Using WebRTC, FilePizza eliminates the initial upload step required by other web-based file sharing services. When senders initialize a transfer, they receive a “tempalink” they can distribute to recipients. Upon visiting this link, recipients’ browsers connect directly to the sender’s browser and may begin downloading the selected file. Because data is never stored in an intermediary server, the transfer is fast, private, and secure. (Your PC must be online while the recipient download the file(s), if you shutdown the PC or goes offline, the download also stops)
You can selfhost it or use the official instance
Syncthing accomplishes both local and Internet transfers and doesn’t need a third party server (if you’re not doing NAT traversal). I don’t think you can send individual files through it’s interface. But you can share a directory and any files you add (or edit) will sync via P2P to other devices.