Is there a setting in Google Chrome that will force it to download media files instead of playing them?

Don't know such setting, but you can Alt + Click on the link, as the Google Chrome Help says.

You can also click on the link as normal and then press Cmd-S once Chrome loads the new URL to save the media file to your computer.

This is useful for e.g., Javascript links and buttons where you don't have the ability to preview the destination URL.

This solution should work in cases when you can't ctrl+click or "Save link as".

1. Download and install the Dionysus extension for Chrome.
2. Go to a page that has links to MP3s on it. You will notice Dionysus will add a little "play" arrow to your browser address field bar.
3. Clicking that arrow will bring up a list of all the MP3s on the page, with the option for you to play them all, in order, or one at a time.
4. To download an MP3 (instead of streaming it), Alt+click its download arrow in the Dionysus window.

If future visitors, like me, are landing here because they're querying how to cause or prevent playback of a file from a direct link to a video it may be worth noting that the Content Type the server declares for the file can play a part

This will auto play in the browser:

Content-Type: video/mp4

This will download as a file:

Content-Type: application/octet-stream