With the latest nightly builds of Firefox this week, H.264/GStreamer support is finally in place for Linux users. With not many web-sites adopting WebM, Mozilla has had to care about H.264 support and now it's available to Firefox Linux users through GStreamer plug-ins. Windows and And Android versions of Firefox have already handled H.264 but now it's finally in place for the next Firefox release, Mozilla Firefox 23.
If using a nightly Firefox binary, the media.gstreamer.enabled preference can be enabled via about:config. Aside from enabling the option in Firefox, the GStreamer libraries must be installed on the system.
For more details on the enabling of GStreamer support in the official Mozilla builds, see this Mozilla.org bug report.