Currently there is no production ready HTML5 only solution for recording video over the web. The current available solutions are as follows:
HTML Media Capture
Works on mobile devices and uses the OS' video capture app to capture video and upload/POST it to a web server. You will get .mov files on iOS (these are unplayable on Android I've tried) and .mp4 and .3gp on Android. At least the codecs will be the same: H.264 for video and AAC for audio in 99% of the devices.
Image courtesy of https://addpipe.com/blog/the-new-video-recording-prompt-for-media-capture-in-ios9/
Flash and a media server on desktop.
Video recording in Flash works like this: audio and video data is captured from the webcam and microphone, it's encoded using Sorenson Spark or H.264 (video) and Nellymoser Asao or Speex (audio) then it's streamed (rtmp) to a media server (Red5, AMS, Wowza) where it is saved in .flv or .f4v files.
The MediaStream Recording proposal
The MediaStream Recording is a proposal by the the Media Capture Task Force (a joint task force between the WebRTC and Device APIs working groups) for a JS API who's purpose is to make basic video recording in the browser very simple.
Not supported by major browsers. When it'll get implemented (if it will) you will most probably end up with different filetypes (at least .ogg and .webm) and audio/video codecs depending on the browser.
Commercial solutions
There are a few saas and software solutions out there that will handle some or all of the above including addpipe.com, HDFVR, Nimbb and Cameratag.
Further reading: