When a car shakes at a stoplight or whenever the car is stopped and it's idling then the most common cause for car to shake when stopped is broken or worn out motor mounts.
The motor mounts are metal but have rubber in between them to act as a cushion to prevent the engine from vibrating your car when in operation.
When the motor mounts become worn out then the motor mounts won't be able to absorb the vibration of the engine and then it will cause your car to shake.
Motor mounts that are broke need replaced soon as you could potentially damage your engine and leave you stranded.