Why would a car accelerate without pressing the gas?

Two things:

The accelerator cable is frayed or sticking. Change it or lube it alot.

Your idle is too high. Have it lowered.

The problem could be some type of vacuam problem. That is what happened to our Explorer. Or maybe a throttle body problem?

if you mean accelerator sticking, I would check the throttle bore. The plate gets heavy carbon build up and should get cleaned every 18,000 miles.

On modern cars, idle is controlled by the Electronic Control Module. An increase in RPM without pressing the gas pedal is called surging. Have the ECM checked for codes and fix the problems it has noted. This should fix the surging problem. On my car, it was the Oxygen sensor. But it could be a number of other things also, including a vacuum leak.

Make sure your floor mat (not even a corner of it) isn't on top of the accelerator pedal. Even the slightest weight can cause the pedal to accelerate enough to be noticeable. The floor mat can slip forward (and has) in two of our new vehicles when we were driving on the highway. It had worked its way off the anchors and slipped forward, causing the vehicles to accelerate.

If it's an automatic transmission, it might be normal provided the engine performance is ok. Auto trannies have a torque converter stall speed. I have a 96 Cadillac Fleetwood and it will move on its own.