The version history below lets you judge just how old a given instance of the Flash Player is and how many bug fixes its missing.
If your browser tries to download a file, Flash is not installed. But current browsers download the file rather than displaying it as a web page.
Update March 28, 2017: I had not used this Flash tester in a long time. I am told that Chrome version 44 and earlier, that support NPAPI plugins, would display this.
In early Feb 2014 it was only displaying the first 3 sections of the Flash version number, which has 4 sections. As of May 2015, the bug was back, it reported only that v17.0.0 was installed.
The bug still existed July 15, 2015 (Chrome on Windows 7 reported that version 18.0.0 was installed).
A Windows user with IE, Firefox and Chrome can have three copies of the Flash Player and each can be at a different version. For many years the update procedure for Flash was manual, rather than automatic.
Now (December 2014) that things are more automated, the problem is inconsistency.
When the installed version is old, it tells you what the latest version is for your browser/OS. The bad news is that it punts on the Chrome browser and IE on Windows 8.
In both cases it says that Flash should be updated automatically, so fuggedaboutit, you're fine.
Websites that need Flash can still use it, but the end user has to first okay this by clicking on the area of the page devoted to Flash. As of Chrome v45, you enable click-to-play with: Settings - "Let Me choose when to run plugin content" radio button.