Neowin spotted that the latest Firefox 27 nightly build introduces "Shumway", a HTML5 Flash Player that replaces Adobe's Flash Player plug-in. So far it's just an experiment but if the effort proves successful it will be integrated in a future version of Firefox.
Shumway is a HTML5 technology experiment that explores building a faithful and efficient renderer for the SWF file format without native code assistance. Shumway is community-driven and supported by Mozilla. Their goal is to create a general-purpose, web standards-based platform for parsing and rendering SWFs. Full integration with Firefox is a possibility if the experiment proves successful.
If you want to test it out for yourself, download the latest nightly from http://nightly.mozilla.org and then navigate to about:config > find “shumway.disabled” and set to false, then disable Flash in Tools > Add-ons. As pointed out, Shumway still has a ways to go before it can fully replace Adobe Flash Player.