Ctl-Alt-F-whatever took a while to clear the screen, but very soon I was able to type "ps aux" to find dozens of Netscapes, dozens of Mozillas, and at least five Galeons rampaging around the CPU. I rebooted after using "killall -12" on all the browsers.
Part of the problem here is the lack of splash screens to pop up and let the user know what is going on. Mozilla seems to have a -splash option, but it doesn't do anything on my machine. Galeon doesn't seem to even have the option. Perhaps we should start complaining about this, as it isn't something that geeks have to worry about on their own machines.