Scattering of light by light: experimental status

This was demonstrated by "Experiment 144" at SLAC in 1997. Here is a list of publications from that project, for instance "Positron Production in Multiphoton Light-by-Light Scattering", whose abstract reads:

A signal of 106±14 positrons above background has been observed in collisions of a low-emittance 46.6 GeV electron beam with terawatt pulses from a Nd:glass laser at 527 nm wavelength in an experiment at the Final Focus Test Beam at SLAC. The positrons are interpreted as arising from a two-step process in which laser photons are backscattered to GeV energies by the electron beam followed by a collision between the high-energy photon and several laser photons to produce an electron-positron pair. These results are the first laboratory evidence for inelastic light-by-light scattering involving only real photons.

I guess you were asking about elastic photon-photon interaction. If that is the case, I remember reading some proposals (and argumentation of feasibility) of experiments using existing laser facilities in:

E. Lundström et al. Using High-Power Lasers for Detection of Elastic Photon-Photon Scattering. Phys. Rev. Lett. 96 no. 8, 083602 (2006). arXiv:hep-ph/0510076

Further references:

J. Lundin et al. Analysis of four-wave mixing of high-power lasers for the detection of elastic photon-photon scattering. Phys. Rev. A 74 no.4, 043821 (2006). arxiv:hep-ph/0606136.

Stephen D. H. Hsu and Brian M. Murray. Thermal gravity, black holes and cosmological entropy. Phys. Rev. D 73 no.4, 044017. arxiv:hep-th/0512033.

I have no idea if the experiments were really made, but those references are quite cool :)

I've a vague memory that light-on-light scattering puts an upper limit on the energy of photons that will propagate over cosmic distance scales. So one probe is very high energy gamma astronomy.