I heavily encourage you to go read the AOPA's NALL report, faasafety.gov, and other industry aviation safety articles and recent communications to pilots about safety. Don't get me wrong, what's being said here are always good things to be keenly aware of; but if you truly want to improve safety you have to address the current leading causes of fatal crashes. Flying today is almost twice as safe as it was 25 years ago, but the record has not improved in the last 10 years. Why? The low hanging fruit was addressed. Drunk pilots are not flying. We've keenly become aware and are avoiding VFR-into-IMC issues to a much greater degree but it remains a problem. However, basic maneuvering skills, CFIT, pilot currency, and loss of control have been stubbornly difficult to address.
Like it or not, the vast majority (and I'm talking 80+% provable, 95%+ actual) of accidents are pilot error. A wing is not going to fall off, and engines seldom explode. The aviation community has been good at addressing these mechanical issues. You need to focus on the pilot issues.
Let's face the facts, GA is not a "safe" activity in the best of days. Fly non-commercial GA 50 hours a year for 40 years, and you have roughly a 2-5% chance of buying the farm, depending on what you fly. Let's see... per hour... flying C-172, equivalent risk of driving a car 18 hours... C-182, 29 hours, GA average, 46 hours. Avoid that piston twin and experimental, they are substantially worse than the GA average. Pick your type wisely, a diamond da-x0 is nearly twice as safe as a C-182, and nearly 3-4 times as safe as a Cirrus. Motorcycle safety is somewhere between the C-182 and GA average, as a point of reference. All assume vehicle fleet average of 27.5mph. And forget that don't jump out of a perfectly good airplane comment... more skydivers perish in jump plane crashes than the jumps themselves...
The good news? Unlike other activities, you are nearly 100% in control of your own safety choices. Mid-airs are very rare. You skills, currency (do _you_ get 1 hr of hard practice/pattern work in each month?), and decision making decide how safe you want to be. Take the hobby seriously, and it will reward you well.
You'll never have the airline level of safety, but you can try to bridge the gap. They fly many hours a month, have professional training, redundant pilots to check decisions, set procedures, weather equipment, turbine reliability, professional dispatchers, and fly between specific and known airports. However, you can try to bridge the gap to commercial safety rates.
The Top 10 Leading Causes of Fatal General Aviation Accidents 2001-2011
1. Loss of Control Inflight
2. Controlled Flight Into Terrain
3. System Component Failure – Powerplant
4. Low Altitude Operations
5. Unknown or Undetermined
6. Other
7. Fuel Related
8. System Component Failure – Non-Powerplant
9. Midair Collisions
10. Windshear or Thunderstorm