One suggested mechanism for damage to health from high-voltage power lines is rather indirect. The lines act like an electrostatic precipitator, putting charge on fine particles of pollutants as they drift past the wires. The result being that the particles are more likely to stick to your lungs when you breathe them in, some way downwind and well beyond the distance where any direct biological effect of the electromagnetic field would occur.

This was published (with empirical evidence that it actually happens) in some honest-to-god refereed journal a few years ago.