Google is adding Chromecast support to the Chrome browser for Android. That means in addition to streaming video to your TV from apps like Netflix and Hulu Plus, you can now visit websites using your Android phone or tablet and if you find an embedded video there’s a decent chance you’ll be able to send it to your TV.
This can also come in handy for web video sites that don’t have Android apps.
As of early March, 2014 this appears to be an experimental feature. You’ll need to install Chrome Beta and enable the “experimental Chromecast support” flag by typing “chrome://flags/” into your location bar (without the quotes) and scrolling down until you see the option to enable the feature.
You could also do things in one step by typing “chrome://flags/#enable-cast” without quotes.
After you restart the browser, you should start seeing a Chromecast icon when visiting some web pages with embedded videos. It seems to work pretty well on YouTube, but results are a bit more inconsistent with other sites such as Vimeo. For the most part what you’re looking for are sites that stream videos using HTML5 rather than Flash or Silverlight.