Edit: Fixed! Looks like there are very many possible causes for this. Mine was one of the more unusual...
I updated SDK Tools to 21.1 and Platform-tools to 16.0.1. Verified with adb version that I am running v1.0.31. My development machine is running Windows 7, x64.
I have four 4.2.2 devices to test with, a Galaxy Nexus with unlocked bootloader but not rooted, and Nexuses One, 4, 7 & 10, all stock.
The Nexus One, being <4.2.2, works just fine with adb, but all the 4.2.2 devices show as 'offline' in adb, and I have NEVER seen the RSA security dialog pop up on the devices, even after several restarts of ADB (using kill-server), the PC and the devices themselves.
Have tried using different USB ports and cables. I'm using the standard 'Android ADB Interface' drivers from the SDK, but have also tried the 'Android Composite ADB Interface' and 'Samsung Composite ADB Interface' drivers too. I even completely re-installed the SDK from the ADT bundle.
Weird thing is, my colleague can get the popup to show on those same devices without any trouble. I even copied his adb.exe and dll's and tried that and it still wouldn't work on mine. He didn't install from the bundle; he installed ADT into Eclipse, the old-fashioned way, but I doubt that would make a difference. What gives?!
Edit 26/02/2013, 16:41 GMT: An update to Platform-tools 16.0.2 was just released. Hasn't updated ADB (still v1.0.31) and still seeing device as offline, and no RSA security popup in sight.
It turns out I had my ANDROID_SDK_HOME environment variable pointing to an old location which no longer existed. It hadn't caused any other problems (strangely) but it appears to have been preventing the RSA authentication process from happening. Probably should've seen it when I was checking the PATH variable the other week, but never mind.
I found the strange location by running the following and checking the readout:
adb kill-server
set ADB_TRACE=all
adb nodaemon server
After updating the location and restarting my PC, it's now working just fine. Thanks to all who responded.