Neutrinos have Mass!

1987A supernova remnant near the center

Neutrinos are produced in several different ways: natural radioactivity here on earth; nuclear reactors; in copious quantities in the Sun and other stars; in supernovas (Wikipedia SN1987A article); and in the Big Bang (though these have yet to be detected, there's indirect evidence here Neutrino ripples spotted in space). In all cases they are ghostly particles, very hard to detect.

The Super-Kamiokande detector, half-filled with pure water. (Courtesy of the Institute for Cosmic Ray Research, the University of Tokyo.)

They were postulated theoretically by Wolfgang Pauli, but it took many years to actually find them.
For a long time one of the great mysteries of physics was the "Solar Neutrino Problem" - the actual number of neutrinos we could detect from the Sun was about a third of the expected flux. This was finally resolved by oscillations among the three types of neutrinos (hence the 1/3). This seems to imply, theoretically, that neutrinos have mass - which has yet to be measured, though it must be very, very small. Until the oscillations were discovered, it was usually assumed that neutrinos were massless, for both theoretical and experimental reasons.
Here are two "popular" articles by John N. Bahcall of Princeton:
Solar Neutrinos: A Popular Account and Solving the Mystery of the Missing Neutrinos

The three years 2001 to 2003 were the golden years of solar neutrino research. In this period, scientists solved a mystery with which they had been struggling for four decades. The solution turned out to be important for both physics and for astronomy. In this article, I tell the story of those fabulous three years.

Here's a recent, more technical review of Neutrino Physics in general by Boris Kayser.

There are many interesting questions about neutrinos which still need to be answered by new experiments (from Kayser).

1. How many neutrino species are there? Are there sterile neutrinos?
There's already an experiment (LSND) which suggests that there might be more than three types of neutrinos. If there are more than three types then there are combinations which do not even couple to the weak nuclear force - they would only interact via gravity. These are the so-called sterile neutrinos.

2. Are neutrinos their own antiparticles?
Charged particles cannot be their own antiparticle, an antiparticle must have the opposite electric charge. But neutrinos are, naturally, electrically neutral, so it's possible. It could be, however, that there's another conserved quantity the "lepton number". It's not clear whether there is such a quantity, but if there is, there thould be distinct antineutrinos.

3. Do neutrino interactions violate CP (charge/parity conservation)?
Why does the universe seem to be made almost entirely of matter, rather than equal amounts of matter and antimatter? CP violation occurs in quarks, but that doesn't appear to be sufficient to explain the observed matter/antimatter imbalance. Since we are made of matter not antimatter, perhaps neutrino interactions are the reason we exist!

Let us not forget neutrino poetry, by John Updike no less.