General Aviation flying is statistically similar to motorcycle riding as far as risk. With that being said, you have to look at motorcycle risk...

A dentist on a goldwing riding along the coast highway on Sunday morning is exposed to a certain level of risk (pretty low).

A buzzed 22 year old male who goes downtown on Saturday night on a ninja has a far different statistical outlook

You have to look at the type of flying you do (and the equipment you use). Motorcycle risk level is probably easy to determine, general aviation has a few factors which can sneak up on you. Assuming that you follow the rules and avoid reckless unauthorized manuevering flight, these are the big areas to pay attention to (in my experience).

1) Midair Collision: You will probably not be able to recover from a midair, so prevention is the key. Use flight following where available, otherwise communicate on CTAF or other air-to-air freqs. If you fly in a congested area, consider buying a cheap GA traffic alerter. Ultimately you have to keep a sharp visual lookout, because not everyone uses their radio and/or transponder.

2) Airspeed mismanagent in the pattern (leading to stall/spin). Keep a sharp eye on airspeed...as a new pilot the inherent importance of that is not second-nature to you, you will have to discipline yourself to look at it especially when you are distracted by other things.

3) VFR into IMC...even an instrument rating may not save you if you are not expecting it, don't have good situational awareness, and don't know who to call for help. If you are not planned and equiped for IFR, plan ahead to avoid IMC. If you think you're going to get trapped, contact ATC early and get some IFR charts out so you know MEA's, MSAs, Freqs, etc. Anticipate spatial disorientation...trust the gauges.

4) Wx while in IMC: GA airplanes don't handle thunderstorms and icing well...use all available weather info to avoid these hazards. If embedded CB are reported, don't fly IMC without radar.