[viart]

Chromium browser let's you do this. It is how I stream my videos over chromecast. It also let's you browse your filesystem.

[shutupalready]

I tried Google Chrome (v29 on Windows, fwiw), and it behaves just like Firefox; i.e., it'll render local text or image files but won't play local videos. I didn't try Chromium.

[zants]

You're right that FLVs don't work (it'll simply "re-download" the video). However, MP4s and WEBMs work fine (probably several other formats as well).

[viart]

I'm using Chromium Version 38. It works for most videos but I have had some the audio did not work for.