1) Large and complex systems that are slow to evolve due to being written in languages that are unsafe or are relatively poor in abstraction (in addition to the immense domain complexity). Examples: SQL and/or distributed databases, Paxos-ish systems, Operating Systems, IDEs, GIS, etc.
2) Extremely high performance systems on the fringe of research. Examples: MIP/LP/CP/SAT Solvers, Theorem Provers, Formal Verification tools, Rete-based Rule Engines, Machine Learning algorithms and frameworks, Statistical Samplers for MCMC, etc.
Unfortunately (maybe, I don't really know if it will turn out well or not), most of the hype for rust comes from back-end web developers. That is fine...I'm sure there is some performance to eek out there...but it is also trying to compete in an area where garbage collection has its greatest competitive advantages (namely, long running server processes). The comparative benefit is relatively small.