One problem related to car accelerates on its own has been reported for the 2010 Lexus GS350. The most recently reported issues are listed below.
I was pulling into a parking space, driving very very slowly, about 1 or 2 mph, and my vehicle experienced unintended acceleration, bolting forward very abruptly. I was able to stop the car by applying extreme pressure on the brake for a few seconds. The dealership reviewed the car and said there was nothing wrong. They suggest that I might have stepped on the brake and accelerator at the same time, which they did to replicate the experience. However, now that I have had opportunity to consider that, I don't think I could have effectively pressed both simultaneously to achieve that abrupt acceleration. If that were possible, and it happens mostly in Lexus and Toyota, is it a design flaw which might enable that?.