I've set up my $99 OUYA to do this (mostly). I've installed a native YouTube app on it (YouTube for Google TV) and installed Flash support for the included Android browser. I also wrote a small client/server Android app [1] that allows the client to share YouTube videos, web pages, basically anything URI-based from various apps' built-in "share" UI and the content will appear on the TV (using whatever app is suited for the URI being opened).

[1] http://bhspitmonkey.github.io/VuDo-Android/