Question: I am not looking for a necessarily super-robust solution with a 10-year track record, but for something that can be used in a real applications, and goes beyond just being able to run an Hello World example.

My preference is to run the compiler on the server, so I can compile Haskell code ahead of time. Of course, the solution would need to be more than just a compiler, and enable Haskell code to access the API available on the browser (DOM, XHR…).

Footnote: the projects I have seen so far don't seem to be actively maintained, or to go beyond being able to run "Hello world", or in some case even to go beyond a project description.

Answer: 
While GHCJS does not seem to be actively maintained, [Emscripten](https://github.com/kripken/emscripten/wiki) seems to be quite current.

* Emscripten compiles [LLVM](http://en.wikipedia.org/wiki/LLVM) bitcode to JavaScript.
* [GHC's LLVM backend](http://www.haskell.org/ghc/docs/7.6.1/html/users_guide/code-generators.html) appears to be actively developed.
* Intuitively, to answer the question, the following pipeline might not be very far from "production quality": Haskell lexemes (-> GHC ->) LLVM lexemes (-> Emscripten ->) JavaScript lexemes

I'll admit that this is a speculative post.
There is a list of "most production level" candidates from Yesod: <https://github.com/yesodweb/yesod/wiki/Javascript-Options> (Yesod is a very popular Haskell webframework so they may know what they are talking about)