Chromecast sounds good and all, but not everything you want to watch is on Netflix and Youtube. This won't work for all files by default (notably .avi or .mov, at least on Windows), however Chrome does have the ability to play local H.264 encoded and .mp4 movies and some other formats.
To do this, you can either
1. Ctrl+O > select the file. (credit: deucegort)
2. Drag the movie into a new tab at the top of Chrome.
3. Use the following urls to access your usual Windows or Mac file structure.
For Windows (tested on Windows 8)
For Mac (tested on Lion):
file:/// or file:///Users/
Note: I'm still waiting on my Chromecast; but in theory, this should work...
Also, I'm not a video filetype/codec expert, but I know a few things and I'm having trouble getting .avi movies that I think should play (using the Divx Web Player plugin for Chrome). I look forward to seeing what you fine commenters have to offer as solutions to get Chrome to play your favorite movie filetypes/codecs.
Let's discuss, since I know some of you already have yours.