Here is what you do, throw the little bastard off your screen. Proceed to ignore it entirely...
Until something goes wrong (not like anything would EVER go wrong under Windows), and you can't control-alt-delete... I have the sneaking suspicion that if you could perform the three finger salute with an illegal operation box up you could just do end task on the error message and keep going.

Also, in my experience with IE, half the time that you get an illegal operation you can simply throw it off the screen and continue browsing. I think my record is having 5 illegal operations off the side of my screen - 2 frozen IE windows, and 3 working ones, until it crashed hard and I had to restart.

From my experience the easiest way to make the illegal operations dialog box vanish totally is to stick it as far to the bottom of the screen as possible (so all of the portion of the dialog box that is still on the screen is on top of the task bar) and then click on the task bar. Goodbye dialog box. It'll reappear on top if you have no window active, but it's easy enough to banish again; just click on the taskbar once more.

If you're too lazy to just restart the machine, but don't mind your open programs getting closed, then simply click Start->Logoff in Win9x. Also, as annoying as First-Aid can be, its dialog box that replaces the standard GPF dialog doesn't seem to have this problem.

By George, i think i have this one solved... if you push the dialog box aside, you lose access to the three-fingered salute. But this way, you get access to ctrl-alt-del!
Okay: you'll need:

• Something that lets you list the processes running, and kill them
  
(i use ProcExplorer, available from Adam's Software ( come.to/adamssoftware ).

• A crashed program (which isn't THAT easy to do intentionally)

Okay, BEFORE you click that li'l UIODOD (once you do, it's there forever), launch your process-killer, and KILL that crashed little program (i.e. netscape.exe).
Then, you can dismiss the illegal operation, and it won't pop up -- you can go on with your life.

---

although i have tried this with success on Netscape Navigator's page faults, ymmv.