I’ve been driving since I was 11 (Imagine how big a '89 Lincoln Towncar seems when you’re that age :D… I’m 25 now), and I’ve never been into an accident either. That’s not to say I haven’t had a few close calls or made some mistakes of my own.
I think the cause of most accidents is drivers being caught out by something - whether it is another driver swerving into your lane or sliding on a patch of ice. The point is, as others have said here, to pay attention to as much as you can while you’re driving. No one is perfect, and our minds are totally incapabale of keeping track of absolutely everything going on around us - which is good, because otherwise we’d be totally unable to perform useful tasks.
So, when drivers are approaching your car from any angle, watch their body language and car placement. People, for example, tend to let their car drift slightly towards the direction they’re turning/changing lanes towards. More often than not they’ll look the way they want to go, even if it’s not a shoulder check. If you watch for these cues you’ll often be able to predict what another driver is likely to do before they do.
One other thing I’ve noticed in Edmonton is how terrible people are at sitting in blind spots. If you’re beside someone and you know they can’t see you, speed up or slow down so they can see your car, which they should be less prone to run into then.
If you’re interested in performance driving, I’ll recommend two books to you. One is called “Drive to Survive” by Curt Rich (or let me know the next meet you’re attending, I have it), and any other book that teaches safe motorcycling principles. Why the motorcycle books? Because they often stress the importance of anticipation and accurate vehicle placement to avoid incidents - after all, crashing a motorcycle could well end up in your death, so serious technique is required to avoid this.
One last tip - avoid target fixation. Target fixation is commonly used by police driver trainers to describe looking at an object in the path or intended path of your vehicle. What you need to do in an emergency situation is to look WHERE YOU WANT YOUR VEHICLE TO GO, not at what you are driving towards. Our hands follow our eyes, so if you fixate on something, odds are you’ll hit it - be it a cone, car, or a kid running in the street. Obviously, you have to train yourself not to do this before that knowledge is required. I’m terrible for this, and I’ve been training myself to avoid doing this by using a combination of GT4 and actively practicing on the road.
Other than that - practice practice practice. Especially at a young age, everyone is a terrible driver. It takes experience to learn what other drivers will do and how to react to avoid bad situations. Sorry for the long post.