I'm using in production in more than a couple of places, mostly for back-end heavy apps (ie: not much UI). Works fairly well with Passenger in my cases.
If your requirements fit within what Sinatra can provide, you shouldn't hesitate using it. It's a very straightforward framework and works well. If your requirements are more complex, look at Rails or Padrino, the latter of which is built on top of Sinatra and is actually pretty awesome.