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One clear-cut case are proprietary embedded systems; they usually give you a private fork of GCC. Trying to shoe-horn Rust in there isn't going to be a good time.
A second is if you don't care about speed or correctness at all. That may sound silly, but you'd be surprised at the number of projects that don't need serious engineering, they just need to knock something out and it's good enough, or something that's only ever going to run a handful of times.
Rust isn't very strong for prototyping; it's much more geared toward long-term robustness. So if you're just trying to throw something together quickly, I wouldn't reach for Rust at first. But of course, those quick little projects have a way of sticking around...
More generally, I think Rust's strengths are around performance (both throughput and latency), memory footprint, predictability, and writing robust, maintainable code bases. If you don't have needs in one or more of those areas, there's probably a language that's better suited for your task.
Well, if you've got a taste for bugs, for one thing. ;)
More seriously, it's a hard question to answer. I've found that I enjoy using Rust in a lot of domains where I wouldn't have expected to -- e.g., simple command-line scripts work out really nicely in Rust, and they run fast, too.
But, overall, Rust is definitely focused on producing polished end-products -- if you want to make something temporary that you plan to throw away, Rust is probably not the language for you, at least not right now. (That said, I'd love to see us make more strides towards better support for "rapid prototyping".)
I would also like to turn the question around: if you were trying a project in Rust, and felt that Rust was really not a good fit, I'd like to hear about it, and why. I'm always looking to know what we can improve. =)