Why don't photons collide with each other when traveling towards each other?
Photons in free space act almost exclusively as waves. Therefore, when they cross paths they merely set up an interference pattern for the very brief time of their interaction. No energy is exchanged and the quantum state of each photon is unchanged after they pass each other.
This interference pattern is akin to ripples on water that approach each other, form an interference pattern of peaks and troughs and then continue on their way.
If matter is present where the photons cross, non-linear effects caused by accelerated electric charges may allow the photons to interact. This interaction could be considered a collision of sorts, resulting in exchange of energies with many possible outcomes.
One such outcome is called frequency doubling, where two photons are combined to form one photon at twice the frequency.
Scott Wilber, President, ComScire - Quantum World Corporation
'The strength and weakness of physicists is that we believe in what we can measure. And if we can't measure it, then we say it probably doesn't exist. And that closes us off to an enormous amount of phenomena that we may not be able to measure because they only happened once. For example, the Big Bang. ... That's one reason why they scoffed at higher dimensions for so many years. Now we realize that there's no alternative... '