Owen Campbell-Moore, one of Chrome’s PM’s for Progressive Web Apps and new APIs asked the following question, and instantly Surma (that is the only name we know for him) said “Sockets”

@owencm Network connections. Like writing an SSH client as a PWA.

— Surma (@DasSurma) August 12, 2016

I also threw in my two pennies, and Marcos Ceres asked for use-cases.

@annevk @Paul_Kinlan @DasSurma @owencm I'd still be interested in a good list of fun things that people want to build but can't.

— Marcos Caceres (@marcosc) August 12, 2016

So here is a list of Apps that people have told me they want to build to host inside a browser. It includes client apps but also Services and Servers.

Outgoing connections

The TL;DR is anything normally has to proxy and convert web requests via a web server to another host.

• E-mail client connecting directly to IMAP server, POP3, SMTP without a HTTP/WebSocket bridge
• SSH client - to connect to a server without relay
• RDP client
• IRC client - again to connect directly
• FTP client (and other file transfer clients)
• Video Streaming client - connect directly to RTMP server.
• BitTorrent client (needs incoming data too)
• XMPP Client
• Connect to Bitcoin/Blockchain server
• Multicast client (and server) to stream video to everyone on the Network
• MDNS Discovery service to discover local devices
• Connect to discovered device (such as wifi speakers) and configure (via @annevk)
• Connect to a time server
• Direct connect to MQTT server.
• ADB over Wifi - Someone wanted to use Cyanogen’s way of debugging their Android device and connecting to it
• Connect to DNS service and query it, was to be used for verifying that a record had been set to prove ownership
• Many games that have multiplayer.

Incoming connections

Mostly the TL;DR here is, a server for everything in the above list.

• IRC server
• BitTorrent client
• HTTP Server for simple local testing.
• HTTP Server to host electron style apps (where the server and client are distinct)
• SMTP service (yes - people have asked me that they want to host this in the browser)

If you have any other examples let me know and I can include them here.