What I can highly recommend is the (free) RetroArch app for AppleTV. You upload your legally owned ROM files via a simple web interface and you can just pair your bluetooth gamepad with the AppleTV.

Side node: The same thing works on phones, too. While most of the games are not very fun on a touch screen, I've found that turn based games like RPGs hold up remarkably well.

edit: I'm referring to AppleTV the box, not the service