The Chromecast is often hailed for its web streaming capabilities, letting you Netflix (or YouTube, or Stan, or Presto) binge on the cheap. You can, however, easily stream local files from your computer to these HDMI-enabled dongles as well with the right apps installed -- here's how to get everything set up.
Your Chromecast is controlled by your phone or by the Chrome browser on a laptop, so you need an app that works with either (or both). Plex is one suitable solution (which we've written about before). Set the server software up on your main computer, then use a Chrome browser or Plex's smartphone apps (Android, iOS) to beam your media files to the Chromecast.
As Chrome has both local media playback capabilities and an official Chromecast extension, you can just use Google's own browser to beam your videos to the dongle if you don't mind a rather bare bones (and occasionally sluggish) solution. Third-party Chrome app Videostream offers a somewhat smoother experience for browser casting if you're on a computer.
Returning to smartphones, there are a bunch of apps that will do what Plex does. Videostream Mobile (Android, iOS), VLC Streamer Free (Android, iOS), LocalCast (Android, iOS), and AllCast Premium (Android) are currently some of the best apps that will do the job for you.