On the Rust side, we're working on integrating Emscripten support into the compiler so that we're ready for WebAssembly right out of the gate. Given that the initial release of WebAssembly won't support managed languages, Rust is one of the few languages that is capable of competing with C/C++ in this specific space for the near future. And of course it helps that WebAssembly, Emscripten, and Rust all have strong cross-pollination through Mozilla. :)
If anyone would like to get involved with helping us prepare, please see https://internals.rust-lang.org/t/need-help-with-emscripten-...
EDIT: See also asajeffrey's wasm repo for Rust-native WebAssembly support that will hopefully land in Servo someday: https://github.com/asajeffrey/wasm