Can one create mass from energy?

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.

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

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.