Originally posted by: f95toli
First of all, the photon does not have an antiparticle as such meaning you can't annhilate photons (also, where would the energy go?)
But to answer the first question: yes, sort of. Although the effects is extremely weak and can only be observed at very high energies; i.e. it can't be used for visible light or radiowaves.
Into an electron-positron pair. You can collide an electron-positron pair to create two photons as well.
Here is a Feynman diagram demonstrating the reaction (time can go either forward or backwards on this graph, so you can either collide an electron and a positron to create two photons or you can collide two photons to get an electron and a positron, note that the electron on the middle branch is virtual).
http://www.shef.ac.uk/physics/people/cbooth/eegg.gif
In any case, the photon IS its own antiparticle. This is allowed because it doesn't have a charge; a photon under time reversal is still a photon (but an electron under time reversal becomes a positron).
Edit: And also, OP, you can scatter photons off of each other. However, you can't think of this as classical billiard ball scattering due to the quantum nature of particles like the photon. You're not shooting single photons at single photons and watching them bounce off of each other. You're shooting clumps of photons often, and most of them won't even interact.
Furthermore, even if you do successfully manage to shoot a single photon and a single photon, there is a non-zero probability that they just won't interact at all. Thus, you can't simply bounce a laser beam off of another laser beam.