SharePoint 2013’s Media Web Part now supports HTML5’s video element. However, HTML5 has no specific file format that is supported. The W3C has encouraged in the past a base line support of file format across browsers, but that hasn’t materialized.
SharePoint’s Media Web Part, on the other hand, does have specific file formats it supports. For HTML5, it supports:
asf, avi, mpg, mp3, mp4, ogg, ogv, webm, wma, wmv
The classic Silverlight Media Web Part supports:
asf, mp3, mp4, wma, wmv