Google has taken up development of Flash, calling it PepperFlash. PepperFlash is currently at version 11.8, whilst Flash from Adobe is frozen at version 11.2. PepperFlash is only available for the Google Chrome browser, but it can also be installed in the open source Chromium browser available in the Debian repository as described in Debian Bits and Snips. (I found that the archiving utility that comes installed with Debian XFCE wouldn't extract a .deb file, but the file can be extracted from a terminal with the following command:
dpkg -x filename.deb target-directorySource: Debian Forum.)
Users of Debian Testing can install pepperflashplugin-nonfree.
The Opera browser company have been pushing HTML5 as a replacement for Flash. I notice that a lot of BBC video content will play in the Opera Mobile browser on my Android phone now, I suspect because it is being served HTML5 (Flash doesn't work on my phone). On this test page, Opera in Andoid plays the HTML5 proprietary format.
In Debian, Chromium plays HTML5 proprietary format, but Iceweasel and Opera don't; all three browsers play HTML5 non-proprietary formats. This of course hints at some of the issues around HTML5 video adoption.
Opera users in Linux will have to hope that HTML5 becomes the standard format for web video before Adobe gives up security updates for Flash on Linux, or use Firefox or Chromium to watch Flash content.
Finally, there is an open source Flash player for Linux called Lightspark, discussed on the Debian Forum. I tried installing it, but video content was juddery and crashed frequently, and Flash games were missing visual components. This looks like another project to keep an eye on.
So, for the moment, Flash for Linux is still available from Adobe, and security updates will be available for about four years from now. It's available from the Debian Repository, but no longer developed. If Flash content doesn't work, try PepperFlash in Chromium (or Chrome).
For the future, keep an eye on Shumway and Lightspark.