As I understand it, photons can meander in any direction at any time but due to the way probabilities cancel each other out, they tend to move in a straight line when not in the vicinity of other particles.

However, because EM diffraction is observable at macroscopic scales, the "straight line" thing really is confusing. Growing up, I always wondered how radio waves transmitted through walls and assumed they just went through them when in fact they go around.

Oh, that's really interesting... I didn't know that (I know very little about physics, I'm more of the mathematician kind).

I thought nothing went in a straight line and everything moved in a wave-like motion.

I don't think the wave is related to 3d movement in the case of light... it's not that the photon is going up and down all the time.

I think this explaination is right:

"In electromagnetic wave, it is the electric and magnetic field vector (or amplitude) that is oscillating." (not the position)

from here: http://www.physicsforums.com/archive/index.php/t-186751.html