Can one create mass from energy? Due to $ E =m c^2 $, one can convert mass to energy. A classic example would be matter/anti-matter annihilation to produce energy (photons, etc.).
Can one do the reverse? So could one do something to photons to create mass?
 A: Yes, it is possible to create matter/anti-matter particles from two photon beams. The first successful experiment of this kind was carried out at the Stanford Linear Accelerator in 1997. 
Here's a summary from the NY Times: Scientists Use Light to Create Particles
And here's the scientific paper: Positron Production in Multiphoton Light-by-Light Scattering
A: Mass is energy. It's energy observed from a "center-of-energy" frame. 
So no 'conversion' is needed. A simple thought experiment: capture a photon in a box with perfectly reflecting mirrors. The box will weigh more with the mass increment equalling $E_{photon}/c^2$. This mass increment translates into an increased inertia of the box: accelerating the box with the photon inside creates an imbalance in momentum transfer to the photon in subsequent collisions.
So how come photons are considered massless? That's simply because you can't observe a free photon from its center-of-energy frame (in loose terms: "you can't keep up with a photon"). When the photon is traveling back and forth in a box, you can observe the box + photon from its "center-of-energy" frame, and the mass=energy equivalence becomes apparent.
A: Not many experimentalists here.
Yes energy can be converted to mass and the simplest example is a photon interacting with the electric field of the atom's electrons and generating an electron positron pair. This happens with quite high probability in all interactions when photons go through matter, actually it is one of the ways we  know a photon has been generated in an interaction, as in this bubble chamber picture:


Accelerated charges radiate

We see  photons coming out from the parent electron and positron pair, which lose energy, and the photons  generate new electron positron pairs after a neutral ( no bubbles) path interval.
The interaction is 

The off mass shell interaction with a field (of the atoms in the bubble chamber liquid here) is necessary for conservation of  the four momentum: the photon has mass 0 whereas the pair has at least 1 Mev ( the sum of their masses).
A: The conversion between mass and energy isn't even really a conversion. It's more that mass (or "mass energy") is a name for some amount of an object's energy. But the same energy that you call the mass can actually be a different type of energy, if you look closer. For example, we say that a proton has a specific amount of mass, about $2\times 10^{-27}\text{ kg}$. But if you look into the structure of a proton, about half that mass (or more, depending on conditions) is actually kinetic energy of the gluons.
Of course, that's probably not what you had in mind. To more directly answer your question, it is possible to produce matter from two colliding photons, although the probability is not especially high. You need energetic photons, and lots of them, to create an appreciable number of detectable matter particles. Wikipedia's article on matter creation has more information and links.
A: A charged particle has an electric field (containing electric energy) which itself influences the mass of that particle in the sense that the mass of the particle is higher, than it would be for a neutral particle (a particular example is that of the pions, where $\pi^{0}$ is lighter than the charged pions $\pi^{\pm}$). In that sense one could say that energy effects the mass and vice versa. As Einstein states both are strongly correlated.
