Read "why" they crash. Its generally not due to mechanical failure (rare itself) of any of the components the aircraft needs to fly. Properly maintained engines dont just decide to stop running. Lycoming had some troubles with crankshafts (expen$ive fixes in some cases).
Most accidents (Federal definition of an accident meaning greater than $25,000 damage) happen because pilots simply run out of fuel. The idiot factor in this is simply mind boggling. Prior to each flight if you simply look in the fuel tanks you will see whether or not you're topped off. If you're not an idiot, this wont happen. So the argument goes if this happens to a CFI...If this happened to a CFI i know i sure wouldnt do my BFR with them or work toward any additional ratings with someone (should they even still have their ticket)
Another HUGE factor in general aviation accidents is continued flight into adverse weather. That means a non instrument rated pilot flying into IMC doesn't know what to do and simply flys into the ground. Some of these are genuine accidents and have seen a front encircle several airplanes within 15 miles of an airport, though all aircraft were granted Special VFR clearance and landed prior to the conditions being anywhere near minimums (which they were at not 20 minutes later)
Read some stuff written by Richard L. Collins. You'll find his material in Flying magazine, as well as the Air Facts series and many many many other sources. He often goes into great detail analyzing why airplanes crash and the trends that happen. I assume he's interested in this because he owns one of the if not the worst planes out there as far as fatal crashes per flight hour, a Cessna P-210. Aviation is safe, as with anything there are your fair share of idiots and identifying and addressing certain attitudes will keep you safe and secure. I remember one article written by Collins, addressing 210 pilots and fuel exhaustion/starvation and he said he'd put a 20 or $25,000 deductible on incidents related to running out of fuel. Staying safe is as simple as following the rules, unscrewing your fuel cap and peeking to make sure the lineman filled your tanks to the proper mark (When i worked the flight line i'd always confirm which "tabs" the pilot wanted the fuel level to because that can be up to a 30 gallon difference in some aircraft), and finally not flying where you shouldnt go.