In fact, none of the other selections from the OS X menu will work either. I'm not sure why this happens, but I was able to find a satisfactory workaround that I have not seen here before. Before when this happened, I was going to the Terminal and typing in shutdown now. Well, that was leaving me with three processes running and a somewhat dysfunctional command prompt. After some experimentation, I just typed in reboot at the Terminal. This seemed to gracefully shut down the remaining three processes, and also gave me a restart back to the Aqua login screen. At the Aqua login screen, I was able to select Shutdown as one of the option buttons and finally do a proper shutdown.
I'm not sure if this is just an odd behavior of Jaguar 10.2.8, or if it's just my system. But I'm not a person that wants to do an entire reinstall of the OS unless I can't boot the machine.
[robg adds: I think there's clearly a system issue at work here, and I would recommend at least re-running the combo updater to 10.2.8, if that's still out there somewhere. I don't recall having any such problems on 10.2.8 myself. The hint here is that the reboot command will get you cleanly back to the login prompt, even when everything else seems to be stuck. I don't think we've covered this one here before, but if someone proves me wrong, just let me know and I'll remove this one...]

