One area that I'm hoping WebAssembly will help with is running native extensions in a portable sandbox. That way libraries like nokogiri can be compiled to wasm ahead of time, then executed on a wasm runtime. There will be a perf hit but not having to wait for nokogiri to compile native extensions will be worth it.
I think the ability to run unknown code in a sandbox is probably the most interesting use case. This is particularly compelling in P2P computing projects.
I am really hoping the mobile platforms like iOS offer pure wasm sandbox APIs for this use case. This could be a powerful way to support programmability, app extensions, etc outside of the appstore. It could appease both Apple for security and developers for flexibility.
proponents of wasm claim that the wasm sandbox was designed with security in mind from the very start. From apple point of view they could offer a runtime with very specific and limited permissions and trust that the plug-ins will respect them.