I know of a couple of installations that use jruby in production. It's often coupled with some sort of java service in the backend, so sure, it's used in production.
It's also stable, even though it tends to lag a little behind cruby in some features. The 2.0.0 feature set is not yet implemented fully.
I'm using JRuby in the code I'm developing for my startup, in order to access Java libs I need. The biggest issue has been that it doesn't support Ruby 2.0 yet, which is merely aesthetic at this point for me. JRuby hasn't given me any grief since I got it going.
It's also stable, even though it tends to lag a little behind cruby in some features. The 2.0.0 feature set is not yet implemented fully.