1994 Buick Lesabre Cuts Off Intermittently While Driving Down The Road, Any Ideas?

If you have a three speed automatic transmission, and the car is bucking before it shuts off at slow speeds, it could be a torque converter lock up solenoid that has gone bad. This would not turn on an engine light.
 
But if it is an automatic transmission with overdrive, I would guess it would have to be a loss of fuel delivery or an ignition problem.
 

We had the exact same problem with our 99 Buick Regal GS. It was cutting off over two dozen times in a one-month period.

I'm a female, so I don't remember what the part was called, but I did save the info from the box, so you can call the parts department and find out what the equivalent would be for your make and model:

ACD# 213-151
GM # 10456161

It hasn't given us trouble since, and it's been two years. It's a simple repair costing about $185.

Good luck!