Plugins are being dropped by users and browsers alike, but the Flash plugin is a real problem because there are so many sites that still make use of it. Google's solution was to move the Flash plugin inside the browser's sandbox and run it as a native extension under Pepper. The problem with this solution is that other browsers don't implement a native client API and so this is a Chrome-only solution.
Mozilla's solution is to get rid of plugins in any form, sandboxed or not, and implement the same functionality in HTML. Shumway is the project aiming to replace the Flash plugin. After a year or more of work it seems that it is ready to be added to Firefox and it is now available in the Nightly channel.
Previously Shumway was only available as a browser extension for testing purposes. Now it is integrated into the core of Firefox and will show Flash content without the help of any plugins or extensions. Although at the moment it is disabled by default. It also doesn't support the full range of Flash content.
You can test your Flash content on Shumway with the help of the Shumway Inspector. You can also see some demos of various levels of ActionScript on the Shumway site.
One big advantage of the HTML implementation is that it can be used by other browsers or apps and it works on platforms that Flash doesn't support - like mobile.
Chrome is dropping support for all NAAPI plugins some time in 2014. Firefox is planning to not need the Flash plugin by January next year when Firefox 27 is released.