My 1999 Accord suddenly dies when I'm driving... I just had the ignition switch replaced and it still dies. Any ideas about the problem? And fix?

Replacing the Ignition Control Module (ICM) and coil should solve the problem:

https://www.askmehelpdesk.com/cars-trucks/faq-how-troubleshoot-repair-maintain-hondas-selected-other-vehicles-46563-4.html#post265896

Have a computer scan done to see if there are any codes stored. It could be the ICM, like tx pointed out, or it could be a bad crank sensor.