Plane Crashes seldom happen on my game, on my current save (No cheats), I have only seen one plane crash. (And one near-miss)
Crash: During the credits, a Rustler fell off the bridge during the Gant Bridge scene.
Near-Miss: I was on the LV Ring at the part where it meets the LS Freeway, and a Beagle appeared and nearly flew into a billboard, but it disappeared right before it did so. (The plane was in the centre of the Camera Angle, so it wasn't a case of distance)