Version numbers on open source products are always tricky. You can said that Red5 hasn't had a 1.0 release. Or you could say they've had 5 major version releases. From the Wiki; where are five "Final" releases.
With commercial software, there is often a business reason to get to 1.0 [ready or not]; however open source software does not have such pressures. The fact that it is an active project is enough for most people.
For specific examples, I was pretty sure that Ribbit was using Red5 in the backend; but I don't know how you [or I] would verify that.
Red5 is well regarded in the community as the de facto alternative to Flash Media Server. I would download it and test it for your specific use case.