The car will run fine and then suddenly it feels like you are playing witht he accelarator pedal as if you ar pushing on it and then letting off. Once this starts, when you go to stop, the rpms rev up and the car wants to keep going, even idling it runs 40 mph. If you turn the car off and restart it the issue goes away then reoccurs randomly. Any ideas?

 

Is your cruise control working properly? Disconnect your cruise control.
Does the unwanted acceleration still occur?
Check Accelerator cables for any snags and stuff, lube it. Check the gas pedal assembly and make sure you have nothing interfere with it.
Then I would check the idle air control valve and clean the throttle body. There should be two return springs. Make sure they are not broken.

I cannot imagine another possible cause for what you describe.