There will always be auto accidents whether the car is driven by an actual person or even if it is not. And I don't want to sound impersonal or unfeeling when I say that, but I do believe a certain number of accidents will happen regardless of who is driving simply because cars do pose a certain level of danger. And certainly the current state of the art in autonomous driving is not at complete autonomy (level 5). So yeah I wouldn't completely trust it yet either.

Not long ago, there was a well publicized tragic accident involving a Tesla car that the NHTSA got involved in and investigated. In their report they mention that crash rates have dropped almost 40% since the introduction of their autopilot. As the state of the art in self driving cars continues to get better, I expect it will continue to get safer.

There is a lot of money going into this right now, and I think it is going to happen quicker than most people realize.