Google has been running their self-driving car beta tests for a total of 300,000 miles now, and they have not yet had an accident, according to The Atlantic.
This technology is still at its very early stages and 300,000 miles is not all that big of a sample. According to a "cursory" analysis by Bryant Walker Smith of Stanford Law School, "Google's cars would need to drive themselves (by themselves) more than 725,000 representative miles without incident for us to say with 99 percent confidence that they crash less frequently than conventional cars. If we look only at fatal crashes, this minimum skyrockets to 300 million miles." We're still a long way away from there.
As someone who hates driving, I love the idea of self-driving cars. And it's pretty easy for me to imagine an America two or three generations from now in which every car is electric and self-driving. It's practically privatized public transit!