I think there's some way to go but there seems to be a bit too much misplaced confidence in human ability over this. Computer-controlled can react faster to changes, don't lose concentration, can react to things that humans don't even see, and so on. The potential is there to drastically reduce the risk of accident. Testing has proved promising so far, with so far no accidents (except one that happened when the human took over...)
On the other hand, there are some catches. The software is, apparently, not quite ready yet in certain circumstances -- most notably, inclement weather -- so I wouldn't want to suggest switching now. Just, to give the technology a chance, to keep developing it, and not to get too caught up in the "but what if it crashes?" argument, while at the same time ignoring all the many failings of our current system.
At the present rate I'd expect driverless cars to be really worth considering somewhere in the middle of next decade.