WebAssembly System Interface (WASI) is a standard that is being proposed that gives WebAssembly modules access to system resources (e.g. files, console etc …). The most recent release of Node adds support for WASI, which is a massive step forwards for the standard.
Next up is another non-browser application of WebAssembly. Istio is an open open source service mesh which makes use of Envoy Proxies, which can be extended using WebAssembly modules. This puts WebAssembly right into the core of your cloud platform. This blog post is a great introduction to writing such an extension.
WebAssembly is a great language for fun, play and experimentation. A real favourite of WebAssembly geeks is audio synthesis - this blog post is a fantastic introduction to the topic.
WebAssembly is becoming more and more a viable technology and a useful tool for web-based gaming. The people at Solitaire Paradise have put this in practice by porting their popular iOS App Pyramid Solitaire Ancient Egypt to WebAssembly using Emscripten.