Want to cut your risk in half? Here's a simple one: don't run out of air. There was a great thread that showed that nearly half of all incidents had, as their triggering incident, running out of air.
I don't have a lot of dives under my belt compared to some (I should hit my 100th in August, after 3 years of diving), but for the life of me (pun intended) I really don't get how people get in a situation where they don't know how much air they have. I can tell you continuously throughout my dive how much air I have (in terms of PSI) and how long its going to last given my current situation (thanks to my air-integrated computer). The idea of getting low on air, other than through a total equipment malfunction, is on the low, low end of the list of things that might go wrong (for me).
So there, my risk of having something bad happen to me is now half of what it is for the general population.
So if you're someone who dives so that running out of air is a very low probability event, you've cut your risk in half too. And then you can keep going: dive smart in other respects, and you'll reduce the risk even further.
As everyone points out, you can't reduce the risk to zero, but everything in life is risky. If you read enough incident reports, they seem to fall into a pattern:
(1) Purely medical things. Not much you can do about them, other than stay fit. Yes, having a heart attack on dry land you probably have a better chance at survival than having one in the water, but I'm not wasting my time worrying about that one.
(2) Purely stupid things. ["Jon Doe was on his first night dive. It was also his first cold water dive. And the first time he was using a dry suit." I'm not making this one up: I saw it in a DAN publication. Are you that dumb? Of course not: see, here's a bunch of risks that you've reduced 'cause you're not an idiot.]
(3) The outliers --- things you just can't do anything about.
No sense in worrying about (3). That's life, no matter what you do. Focus on (2), and make sure you stay nicely active so in a pinch, you've got the extra physical capacity you need should something extraordinary happen. There -- now you're part of the low risk category too.