Two incoming photons scatter each other and in the final state there are two photons. This is not a tree level process in standard model because photons have no charge or mass, they cannot couple to each other. However, there are loop induced processes (one-loop level) where this process is possible. Experimental searches presently give an upper bound on the scattering cross section of light by light. (for example PVLAS experiment).

If you are particularly interested in the particle nature of photons, then Quantum electrodynamics tells us that two photons cannot couple directly. However, in some cases (significant probability for very high energy photons) matter can be created. See links below. 

https://en.wikipedia.org/wiki/Two-photon_physics

http://www.slac.stanford.edu/pubs/slacpubs/11500/slac-pub-11581.pdf

In the free space interaction between the two photons will not give any energy transfer between them, so wavelength will not change but in the presence of material at high dense photon-matter interaction, the energy can be transfer between the photons in the presence of material and as a consequence photons wavelength changes. These phenomenon can be studied in the nonlinear optics  

The photon's "wave length" is frame dependent: just move around! Precisely: my photon's wave length is - generally - not yours. 

Two incoming photons scatter each other and in the final state there are two photons. This is not a tree level process in standard model because photons have no charge or mass, they cannot couple to each other. However, there are loop induced processes (one-loop level) where this process is possible. Experimental searches presently give an upper bound on the scattering cross section of light by light. (for example PVLAS experiment).

Send your photon into a medium.

Many of the other proposals here, including the one you indicate yourself, are really conversions; you trade one photon (plus something else) into another photon (plus something else).  You may say my suggestion is a bit like that too.

Besides all the conversions proposed above, there exists also down-conversion: splitting of a photon (if its energy is high) into two photons of lower energy.

But the photon wavelength depends also on the medium inside which it travels. Inside a refracting medium the photon wavelength increases because the phase velocity decreases.

The leading characteristic of light is frequency. The wavelength is determined by dispersion. It changes when the light enters a different medium. It may become imaginary. 

The situation for a photon is different. Photons are defines in vacuum using Born-Karman conditions. That sets the wavevector as the leading characteristic. But it is very abstract notion. Should they be redifined for a half space air, half space metal, for example? In that case they would not even have a wavevector. 

Therefore, the photon defined in the whole space cannot change its wavelength. Interacting it can be absorbed with emission of another photon.

IMHO, its better to work with light.

In general relativity, a photon's wavelength can change with respect to spacetime geometry.

I would argue it is very difficult to give clear meaning to the statement: it is the same photon. However, if I have an EM field resonating in a cavity and I slowly change the cavity's dimensions, I would assume all the photons in the cavity collectively change their wavelength. For this to work, the resonant modes should be well separated in frequency, so maybe microwave resonator would be best. Of course, the photon interpretation then is a bit strange, but photons are always a possible correct description of any EM field.