93 Lumina cuts out

I am original owner 93 Lumina, 3.1L V6, 155,000 miles. The last several weeks the engine cuts out while driving, or pulling out from a stop sign. It will sputter, then die immediately. In Park, the engine turns over but won't start. After several tries it finally starts, then runs fine. This happens very sporadically. I can drive for days, on the highway or city, and it runs fine. Then it may cut out while driving the next two days, then it runs fine for several days. It has cut out while I was driving at 60 mph, I pulled out to pass, hit the gas and it died. Other times it will die while pulling away from a stop sign or light. No warning, no dash lights. I have always done 30,000 mile tune-ups/maintenance. My mechanic is lost; there are so many sensors, etc.

When this happens you need to check for fuel and spark, take a can of carb cleaner with you when it dies spray some into the intake, if it starts it is a fuel system problem, if not most likely an electrical problem, such as a crank sensor or coil pack module.

This is a definate sign of failing igniton module and/or crank sensor as stated. Both go out and act similar. Will get worse as time goes along. Have the ignition module/coils removed(they come out together) and have module tested at most any parts store such as NAPA or Advance. Take less than a minute to test. If bad go ahead and replace. If not, the crank sensor is cheap and would be the next best thing to try. My friends Corsica (same motor) had BOTH fail at same time. Acted just like this. Very common problems for these cars.
Outside chance it is a fuel pump issue, have it tested for pressure and be sure to change the filter regardless of what you find.

I agree with jsgold, you have the classic symptoms of a crank position sensor or ignition module faulure. I'd bet on the crank sensor, but both exhibit the same symptoms.