I have spent a good part of my career trying to figure out how to improve transportation safety. My actual employment has been in surface modes, but there are a lot of common themes. The most disciplined environments prove safest. Only you can answer how safe you are at heart. The FAA's ideas such as I'M SAFE can be a start. I had come up with my own similar approach-three trikes and it's off. If three things get significant adverse attention from me, I call off the flight. These change based on how good I feel about my skills.
I have noticed that accidents that do not involve deliberate disregard for basic principles, like VFR into IMC, stretching your fuel, overloading the aircraft, or buzzing, usually involve a causal chain that causes the person in control (pilot, engineer, driver, conductor, etc.) to overlook events that become part of the causal chain. I can overlook one thing or even two, but once three things are getting my attention, I am much more likely to miss the building circumstances. Examples of the kinds of distractions I am talking about could involve a really hot day that causes me to be really uncomfortable preflighting the aircraft, a traffic jam on the way to the airport, especially if it is unexpected and I have some kind of deadline, an argument with my kids, bad health news from my parents, an excessive mag drop that only goes away after I run the engine very lean to clear off the plugs, bumping my head on the flaps or ailerons, or any of a host of things. I know what is on my mind.
So, if I avoid violation behavior, and avoid things that might distract me, the next question is how best to prepare. I have decided to get X-Plane and use it to practice my navigation and related skills. I can even use it to simulate some emergencies that would not be a good idea to practice in a real airplane. It's not a perfect answer, but I believe I can use it economically to enhance my skills.
I also think a program of instruction is a good idea. My flying club has plenty of requirements, but simply trying to enhance one's skills is a good idea. I think that there are three groups of skills: Decisionmaking, technical, and kinesthetic (stick and rudder). I discussed decisionmaking above, and at the moment the FAA is going all out on the topic. I think the simulator has the potential to help my technical skills. None of those skills keeps you out of trouble if you can't fly the plane.
There has been a lot of discussion of stick and rudder skills, but the question is how do you develop them. I think that some training in aircraft that are relatively demanding of such skills, like cubs or taylorcraft, area great idea. I also think you should practice spins, and other similar maneuvers, but some maneuvers really let you know how good your skills are, such as falling leaf, lazy 8, and chandelle. Another great indicator is the precision of your landings. How well do you stabilize the approach, do you touch down where you wanted to, how well did you control your speed, were you in the very center of the runway, were you drifting laterally at all, and how much runway did you use? If you are unhappy with your performance on any of these counts, try to figure out why, and do something about it.
Go read lots of accident reports and see where your skill set would not have kept you out of the trouble the accident pilot got into. Set up your personal accident prevention plan and seek out the training or other improvements that will keep you out of the accidents.
Finally, be aware of what economists call "time inconsistency of preferences." Learn to set your parameters ahead of time and live within them. I think a very common mistake in using GA for transportation is mistaking en route speed for some kind of measure of logistical effectiveness. If you need to be a some place by a certain time with 95% confidence, in GA you have to allow a lot more time to account for things like weather and maintenance delays. For example if I had a business meeting in Atlanta at 9 AM a week from today, and I live in the DC area, I might have to leave earlier by GA aircraft than I would by car to ensure a 95 percent chance of being there on time.
I don't think it is physically possible for an average GA pilot to come close to the kind of safety record the airlines have. I do think it is feasible to reduce risk to no more than 20 percent of the GA average per hour.
Many transportation carriers have accident rates well below industry averages. My observation is they get that way by consistent emphasis on safety. Motor carriers have wider disparities among them than do rail carriers, but in both industries it is the constant emphasis on safety that bear fruit. If you are willing to live with your own discipline, then you too can be much safer.