Firefox 20, currently in the Nightly channel, now offers support for H.264 video as well as for AAC and MP3 audio. It's not enabled by default and support is considered experimental, but it's there.
Mozilla is moving forward with native support for H.264 videos in Firefox. It's been a long time coming, or rather, it hasn't, as Mozilla initially had no plans to support patent-encumbered technologies in its open source project.
It held out for as long as it could, but with Google and everyone else abandoning the fight, Mozilla decided it was time to give in and add support for H.264, along with AAC and MP3 in the process.
The codecs won't be built into Firefox, for a multitude of reasons, which means the browser has to rely on whatever support the operating system it's running on provides.
Firefox for Android already supports H.264 via the built-in software and hardware decoders, now Firefox 20 on Windows 7 and later versions, does the same. Mozilla's still working on Linux and Mac support.
The feature is hidden behind a flag, you have to visit about:config and set "media.windows-media-foundation.enabled" to "true" to see it in action. You can visit HTML5 Test to check whether it's working.