To find out which version of the Adobe Air run time you have install is easy to find. I am using Mac OS X (Snow Leopard) so your path on another operating system might be a little different.
Open the the file /Library/Frameworks/Adobe AIR.framework/Versions/1.0/Resources/Info.plist in your favorite XML editor, and locate the <key>CFBundleVersion</key> entry (line 19).
The corresponding string below this entry (line 20) represents the version of Air, for your system. <string>126.96.36.19910</string>
Therefore on my Mac I am running Adobe Air version 188.8.131.5210
<!--?xml version="1.0" encoding="UTF-8"?--> CFBundleAllowMixedLocalizations CFBundleDevelopmentRegion English CFBundleExecutable Adobe AIR CFBundleIconFile Adobe AIR CFBundleIdentifier com.adobe.AIR CFBundleInfoDictionaryVersion 6.0 CFBundlePackageType FMWK CFBundleVersion 184.108.40.20610 NSHumanReadableCopyright Copyright © 2007-2010 Adobe Systems Inc.
My next task is to create an Air application that checks this!