I haven't dug into WebAssembly or asm.js yet. There is a huge amount of potential, though. We wouldn't have to target JavaScript if we want to develop for the web. Instead you could transform to WebAssembly directly from your source language. I can see this could be a huge thing performance-wise and probably a great thing for language developers too.
I think JavaScript will remain relevant for quite a while. WebAssembly just might open new opportunities to developers. It might also bring more people to the platform and keep the scene vibrant.
I would need to experiment more to give a more specific answer. But overall I see WebAssembly as a good step given they have gotten major browser vendors on board. We have seen efforts like Dart earlier, but they failed due to the lack of support.
It's not enough if only one vendor is behind a technology. You need the biggest ones. Even SVG was stalled for years because a single vendor was missing. If they can avoid that with WebAssembly, it can work.