Umbran's covered a lot of stuff, so I will be relatively brief compared to my usual rambles. Just wanted to go through a couple more basic issues right now.
There's a question upthread about the difference between matter and antimatter and whether antiparticles have the opposite spin than normal particles. I'll just add a couple of things to what Umbran has said, which is first of all that each particle has an antiparticle. In some cases, the antiparticle is the same as the particle itself; this is the case for photons (quantum particles of light). As Umbran said, the "charges" of antiparticles are always opposite of the corresponding particles. That includes electric charge but also more mathematically abstract things. For example, the neutron is electrically neutral but has "weak charge," so the antineutron has opposite "weak charge." (I am grossly oversimplifying that.) Quarks have three types of "strong nuclear force charges" a.k.a. colors, known as red, green, and blue, but antiquarks have anticolors, which you might colloquially call cyan, magenta, and yellow.
Spin is a little more complicated in that it's a more technical definition. But, using suitable definitions of "spin" and "antiparticle," yes, they have opposite spins. This isn't too big of a deal, though, as most types of particles can spin in either direction, which means their antiparticles can too. Neutrinos are a bit weird, however. Neutrinos can only "spin left" (technical definition), which means antineutrinos can only "spin right." Theoretically, "right-handed neutrinos" could exist (and could explain some puzzles about neutrinos), but they don't interact with any types of particles we know about, so we've never been able to observe them.
Umbran said:
So, say we have a *really* energetic photon. Rather than just fly along forever, it may at some point spontaneously create a particle-antiparticle pair out of its energy. Say it creates a positron and electron. The electron has some angular momentum intrinsic to it. In order to conserve angular momentum at the moment of creation, the positron must be created with the opposite angular momentum. In that sense, we may say it has the opposite spin.
Just want to correct this quickly. A photon can never just split into an electron and positron because that would violate energy and momentum conservation. A photon that hits something, though, can create an electron and positron. Photons also have intrinsic angular momentum (spin), and total angular momentum coming in always has to equal total angular momentum coming out. So keeping track of spin is important in calculating particle interaction possibilities.