I have a 2001 Honda Accord with approximately 181,000 miles on it. It runs great but about a week ago the car died, without any warning signs, while I was stopped at a stop sign. It started right back up and I didn't have any more problems from it until yesterday (a week later) when the car suddenly died while I was driving down a road. Again, it started right back up. My check engine light is not on and both times the car died without any warning or stalling; it just suddenly, randomly, died. Any ideas what could be causing this or what I should get fixed?

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

If the problem persists, replace the main relay. Because of the mileage on the car, I would replace all three components. Then, you should be good for another 120,000 miles.