VLC is an awesome, open source local media player for Windows and Mac that plays just about any media file you throw at it. It isn’t available for Chromebook – currently, the best you can do for local media files is the built in media player.
Chrome OS itself
Chrome OS has a basic music player built into it. Really basic. It will read MP4 movies, MP3 and OGG audio files (full list here), but if you have AAC, FLAC, WMA or any other file format you’re outta luck.
It turns out that the Google Drive viewer supports a wider variety of video files (full list here), so if you’re having no luck with the built in viewer, you can upload the file to Drive and try to watch it from there. Note that if your your file is very large, the upload can take a very long time, so this option is best for smaller files.