Luckily, I've never been involved in an accident.
I know it's impossible to control others' actions on the road, but I think it's possible to minimize the potential for an accident by always driving defensively. I've been driving for over six years and have amassed over 120,000 miles on the road, and I've never so much as received a scratch on my car.
I did have a few close calls when I was starting out driving -- like I suspect most drivers do -- but I was able to learn from all of those.
I found that if you drive as if everyone else around you is an unpredictable, terrible driver, you'll likely end up being safer. You can predict what each car might do and be very situationally aware.
The only time I was in any accident ever was in a school bus in high school -- someone thought they could beat the bus by pulling out at a side road while the bus was on the main road. The person in the other car didn't make it and scraped the side of the bus.