The Rust language is intended to reach version 1.0 soon (either before the end of the year or early 2015), which comes with the promise of being backwards compatible. However the Rust standard library is still undergoing stabilization and parts of it may still change for a while. Right now a lot of work is being done in that area, to stabilize the most important bits.
Mozilla is also working on Servo, a research-project to develop a browser engine in Rust. The goal is to experiment with more parallelization in the browser, and Rust is supposed to help by making it easier to write correct multithreaded code. To do this Rust has a strong focus on ownership of data.
Rust can run without a runtime and the standard library is split up into several parts (which is not invisible to users of the standard library) that can be used separately when you choose to compile without the standard library. The advantage is that when you target, say, a platform that does not support dynamic memory allocation, you can still use the parts of the standard library that do not require allocation (liballoc). Or you can go without libc bindings. So it is relatively easy to run Rust on bare metal. You could write an operating system in Rust if you wanted to (and I think some people are trying to do just that, but I haven't heard from them for a while).