HTML5 video
Support for HTML5 video has been steadily increasing. In June 2013, Netflix added support for HTML5 video. In January 2015, YouTube switched to using HTML5 video instead of Flash by default. In December 2015, Facebook switched from Flash to HTML5 for all video content.
Use of Ogg formats in HTML5
CTO at Opera Software, Håkon Wium Lie explained in a Google tech talk entitled "The  element" the proposal of Theora as the video format for HTML5:
After the presentation, Lie was asked whether Opera will support other formats than Ogg: