Rust is intended for applications where you need speed, concurrency, and safety/correctness. In some senses, "use Rust where you would use C or C++" makes sense, but we're also seeing a lot of usage from programmers who have rejected C or C++ for various reasons.
One angle that we've been focusing a lot on lately is productivity. Think about some feature of Rust that provides safety, like out borrow checker, which ensures that pointers don't do bad things. One way to think about this is safety, but another way is productivity: if your application segfaults, you have to track down what actually caused it, and then what caused the cause: "oh this pointer was null because I did something incorrect in this other part of my code." While having the compiler do these checks can sometimes feel like a productivity _loss_ at the beginning, you do a lot less debugging later, so it's a productivity _gain_ overall. (Or at least, we feel that way.)
Other features of Rust make it feel productive as well: a focus on iterators and composable iterator adapters is often more productive than manual for loops, Cargo and crates.io enable wide-spread code re-use[1], we've been working on good tooling for IDE integration for those that use IDEs, and "zero-cost abstractions" help you have nicer interfaces while not having to pay the cost for them. Like this: https://news.ycombinator.com/item?id=13117608
One interesting area where we've seen lots of production Rust usage is embedding Rust in other languages. Since Rust can expose functions that look like C to the outside world, you could write a Ruby, Python, Javascript, or whatever extension in Rust instead of C. And Rust's safety features are appealing here, since you may not be the kind of person who writes C all the time: that's why you write Ruby/etc in the first place.
Soon, we expect to see more usage of Rust on the server: the "tokio" project is gearing up for an initial release, which provides a foundation for asynchronous IO. Even before tokio is released, people are playing with this: crates.io is Rust on the backend, and "npm recently began replacing C and rewriting performance-critical bottlenecks in our registry service architecture with Rust": https://medium.com/npm-inc/npm-weekly-73-no-love-for-http-ur...
Basically, lots of places. We'll see how things go into the future!
1: Anecdote time: my favorite package is https://crates.io/crates/x86, which provides low-level bindings to various x86 platform details. Writing an operating system? No need to define your own IDT entries, just grab the library and http://gz.github.io/rust-x86/x86/irq/struct.IdtEntry.html has you covered. Re-usable packages in operating systems is super cool. On a higher level, this kind of thing is enabling Firefox to re-use Servo components more easily; Firefox can just pull chunks of servo with (relative) ease.