Can two photons be converted to one photon of higher frequency? Is there a process which can convert two photons of energy $E_1=h\nu_1$ and $E_2=h\nu_2$ into a single photon of higher frequency and energy $E=E_1+E_2 = h (\nu_1 + \nu_2)$? How about converting $N$ photons into one photon of energy E=$\sum_{i=0}^N h\nu_i$?
 A: Photons don't interact directly.  However, you can do exactly what you want if you're willing to bring material to the game.  An atom can absorb one photon, exciting it to a higher energy state.  It can then absorb another, bringing it to an even higher state.  It can then emit a single high energy photon to drop back down to its original state.
Another interesting solution arises from non-linear optics.  A very common case of what you describe arises in green and violet lasers.  A common way to generate those colors is to start with a Nd:YaG laser at 1064nm or a Ti:Saphire laser at 800nm and pass it through a "frequency doubler," which is a material exhibiting non-linear optical properties.  The result of these non-linearities is a 532nm (green) or 400nm (violet) product.
A: There is combined two-photon absorption and second harmonic generation: http://epub.uni-regensburg.de/3957/1/ubr03451_ocr.pdf
Which is a process that allows just what you are looking for.
Also photon-photon scattering is possible by virtual particles, which could (in the inelastic case) lead to similar results also known as photon acceleration in vacuum. Here is a document describing that process in detail:
https://edoc.ub.uni-muenchen.de/19887/1/Boehl_Patrick_Albert.pdf
