I have been spending the last few weeks working on an Amazon Echo app to create a voice interface to Plex.
You can do simple queries, like "what's on deck," but far more interestingly you can actually request a particular show or episode to start playing on your Plex client.
Here's a demonstration video of the first proof of concept:
I've been doing a lot more work since then, and now have support for playing a specific episode, confirming the show if Alexa is unsure that she heard you right, and a random high-rated (top 10%) episode.
I'll be creating a new demo video once I get all of my 1.0 features in, and then it'll be on to multi-user support so that this can actually be published and made available on the Alexa app store.