I've used Rocket and Actix for production web services. I love Rocket's conciseness; however, it still has a nightly dependency, and is still in the process of updating to async. If you can live without those two things, I'd highly recommend rocket.

Actix is one of the most mature but (in my opinion) complicated for someone to stand up when just standing up a simple web service. It's extremely performant though.

I'd look into tower and warp too if I were you - they seem to be almost as concise as Rocket, but have no nightly dependencies and already have async support.