Datalog is sometimes used as an alternative to SQL. Prolog is used by researchers experimenting with rule systems (e.g. type systems, theorem provers, etc).
Mercury has been used to write regular desktop software, with a couple of notable successes.
One way to think about Mercury is that it’s like Haskell, except it’s so declarative that the functions can run backwards, generating arguments from return values! Obviously that comes with some pretty big caveats, but in many cases it works great and is extremely useful.
I believe Mercury is intended to be comparable to languages like Java, C# and Ocaml, in terms of the performance profile and generality. I don’t know what it’s like in practice though.
I view it more as a fascinating proof of concept than a language I’d actually like to use. Really I just want new projects to steal ideas from it.