Having got that out of the way, the HTML5 spec for the VIDEO tag is a bit tenuous at the moment. Though the API is laid out in full, there are essentially three competing encodings vying for the default: Ogg/Vorbis, MPEG-4, and VP8. Only Mozilla supports Ogg as other parties feel uncertain about its defensibility in a patent war against MPEG-LA. MPEG-4 is not F/OSS, ergo Mozilla isn't supporting it. Google has purchased and opened VP8 in hopes that it will become the open standard, thereby assuaging Mozilla's and the F/OSS' community's fears, though Apple has yet to be sold on VP8's defensibility again MPEG-LA.
To wrap this up, if you do a little digging you'll find that Apple used the MOV container to hold an MPEG-4 video. This is just fine and dandy in the current state of the spec, though it would have been nice for Apple to use a different container format.
Also, both Google Chrome and Opera support Ogg Theora video, not just Mozilla. The only ones claiming to be worried about patents are the well known supporters of open technology at Apple and Microsoft.
Chrome/Chromium and Opera also support Ogg Theora/Vorbis out of the box.