I notice you left C, JVM, and .NET off the list. What's the story for how you could run Rust on a JVM, or on a platform that has nothing but a C compiler?
The compile-to-C case is the most straightforward of the three you mention, but also the one I'm most skeptical of. I do understand that there are some venerable old and/or small platforms where C is the only option. I don't know any specific examples of what people want to do by transpiling to C though. The only thing I know with any certainty is '8-bit microcontrollers', and this is one case that Rust is likely to be a tough fit for (largely because it wants pointer-sized things to be 'big enough', as well as other reasons I've forgotten).
Still, if it's necessary, it can be done with great effort (see the perennially broken LLVM C backend), but it's very low priority as of now.
I'm not sure yet the role of a JVM/.NET backend for Rust (besides the coolness factor) and I don't think people have put a great deal of thought into it. What we will have though is easy ways to bridge between the managed runtimes and Rust for accelerating your managed code or binding to system APIs. This will be necessary for creating decent Android/Windows environments.
(On the .NET topic a MSIL backend would also get us non-asm.js JS via [JSIL](http://www.jsil.org/) which would give Rust access to the DOM. This is quite a flight of fancy though).
That is what most people want it for anyways.
If C is the output of the compiler, then we speak of a C Backend, which means the part that transform the final IR in the other language we want to translate to (eg: x86, arm6, sparc, ... C :)
As a final note, it's likely that platforms so conservatives that they only provide a C ansi compiler, will not be aroused by Rust.
(I personally wonder if the MIR work mentioned elsewhere in this thread would allow for creating a simple compile-to-C backend without too much effort.)
I can believe that the Rust toolchain is pretty portable. But it's also big. Say someone wants to install my software on some weird platform like, say QNX. I'm not comfortable saying that step 1 for installing my (relatively small and simple) thing is: install the (very large and complex) Rust toolchain.
I want to be able to ship C source that will compile anywhere. Though I am comfortable needing two separate C sources: a 32-bit source and a 64-bit source.