Particles and Antiparticles
Associated with any particle is the corresponding antiparticle. Theoretically, the existence of antiparticles has been shown to be a consequence of the theory of quantum mechanics combined with Einstein's theory of relativity. It is known under the name CPT theorem. An antiparticle can be defined by the fact that if taken together with the particle one obtains something that has no properties except energy. No charge, no spin, nothing.
A particle may be equal to its antiparticle. An example of such a "self-conjugate" particle is the photon. Another example is the π0 which is a spinless bound state of a quark and an antiquark. Not only elementary particles have antiparticles, but also non-elementary particles, such as the proton, have their anti-companion. They are simply made up from the corresponding antiparticles.
The W+ and W- are each other’s antiparticles. The photon and the Z0 are their own antiparticles, and the antiparticle of any gluon is simple another one of the gluons. For example, the anti-version of the red-antiblue gluon is the blue-antired gluon. The graviton (zero mass) is its own antiparticle. This is the only known spin 2 particle. Although the gravitational field is of course well known, it has not been observed directly.
Neutrino
If the particle has no mass and moves with the speed of light then “handedness” is not a relative statement. You have particles that are always left-handed. If it is massless than the neutrino is such a particle. The interactions are such that always a left-handed particle is emitted, i.e. the spin is always counter-clockwise in the direction of motion. The antiparticle is always right-handed. The spin flips direction when passing from particle to antiparticle.
If you see a particle decaying into a neutrino / antineutrino pair (flying off in opposite directions) then you know that the particle has spin 1. Thinking in an opposite way, when you collide a neutrino with an antineutrino in the opposite direction the spins point in the same direction. There is actually such a spin 1 particle, called the Z0. It indeed decays some of the time into a neutrino-antineutrino pair. These statements are subject to change if it is found that neutrino have mass, and thus do not move at the speed of light. In that case you could, by going faster than the neutrino, turn a left-handed neutrino into a right-handed one.
Despite the fact that neutrinos are neutral the antineutrinos are different from the neutrinos: they are not their own antiparticle. They have different handedness. Furthermore, neutrinos have lepton number 1, and antineutrinos have lepton number -1, which means that some reactions are possible with neutrinos but not with antineutrinos and vice versa.
Elementary puzzles
Color of three
The greatest puzzle of elementary particle physics today is why are three families? Having only three families and no more makes it virtually impossible to see them as bound states. A further problem is presented by the three neutrinos. For all we know their masses are zero (or very nearly so). The difficulty is that no one knows of any way to have a bound state such that the mass of that state is zero. Up to now most people thought that neutrinos are massless, but certain recent experimental facts suggest that neutrinos have (small) masses. If so these masses are less than the known limits.
Masses
Here is another major problem of elementary particle physics. Where do all these masses come from? Why is the top-quark so incredibly heavy? Why are neutrinos massless (if they were)?
Spin 0 - Higgs boson
Experimentally we have never encountered any elementary particle that has spin zero. There is a hypothetical particle, the Higgs boson, that supposedly has spin zero, but this particle has not been observed so far.
