Single page apps and drop-in components that you can let run in a div. Graphics and games work well, too. I like it as a bit of sanity in the front-end world - its type system and syntax are comfortable for me.

Its static dataflow graph approach to UIs is a good story, and the standard component factorization (the Elm Architecture) makes it easy to get productive in a weekend. It was a good enough story that Redux reimplemented the ideas in a JS + React context.

The virtual dom approach doesn't play nice with jQuery-style shenanigans, so the JS part of common JS/CSS libraries like Bootstrap aren't really usable directly from it, unfortunately. I'd expect React has the same issue, but I haven't really played with React to know for sure.