Actually, we can't say for sure. The technique used by Super-Kamiokande (neutrino oscillations) does not tell us the mass, only the difference in masses between two different types of neutrinos (actually, the difference in the squares of the masses). However, if there is a difference in mass between two types of neutrinos, at least one type (and probably all of them) must be non-zero.
From a practical standpoint, the difference in mass we measure gives us a good indication of what the approximate mass of the neutrinos are. The heaviest neutrino probably has a mass of about 0.05 electron volts, or about one billionth the mass of a proton.
In science, it is a given that new evidence may eventually be found which changes our understanding, so scientists rarely admit to being absolutely sure about very many things, especially new discoveries. However in this case, we are quite confident that neutrinos have mass. The phenomenon of neutrino oscillation which we observe is only possible if neutrinos have mass. Five different types of data, including data from neutrinos made on earth and in sun, show the characteristics of this oscillation. All five sets of data have been independently analyzed by two groups within the experiment, to reduce the chance of experimental mistakes. In all cases, the independent groups found results in agreement with each other. The chance of all these effects being due to a statistical fluctuation (i.e. random chance) is much less than 1%. A variety of theoretical predictions have been tested, and only neutrino oscillations (and hence neutrino mass) appear capable of explaining our data.
Missing mass and dark matter are two terms coined to explain puzzling observations in astronomy. In observations of distant galaxies, there appears to be more gravitational attraction between nearby galaxies, and between the inner and outer parts of individual galaxies, than can be accounted for by the visible objects (stars) making up the galaxies. Since gravity is the result of attraction between masses, it therefore appears that there is some unseen (missing) mass which is adding to the gravitational forces. Since this mass is not emitting light (otherwise it wouldn't be missing...) it is also called dark matter.
Neutrinos have been frequently suggested as possible sources of the excess gravitational forces observed in distant galaxies, but they can only play a role if they have mass. An enormous quantity of neutrinos must have been produced in the first instants after the Big Bang. These relic neutrinos have not been directly detected, but a similar "sea" of photons leftover from the Big Bang was discovered in 1965 by Penzias and Wilson, and has since been studied in detail (this is the so called microwave background radiation).
Now that the existence of a neutrino mass, and an estimate of its value, are known, there will no doubt be renewed study of the cosmological influence of neutrinos. It can be said with some confidence that the small neutrino masses indicated by our data are probably insuffient to account for all the missing mass. However, theoretical calculation of the effects of massive neutrinos will no longer have to speculate as to whether neutrinos do, in fact, have mass.
The same cosmic ray reactions in the upper atmosphere which produce the atmospheric neutrinos measured by Super-Kamiokande also produce particles called muons. If the experiment were at the surface of the earth, so many of these cosmic ray particles would be passing through the detector that it would be impossible to observe anything else. Muons are charged, and while they do not penetrate matter nearly as effectively as neutrinos, they do sometimes have sufficient energy to reach considerable depths. Even about 1 km underground, Super-Kamiokande approximately three such particles pass through Super-Kamiokande every second. But by going underground, we ensure that 99.9% of these muons are filtered out by the rock above us.
The very nature of neutrinos makes practical applications unlikely in the forseeable future. The goal of the experiment is to improve mankind's understanding of the fundamental building blocks of nature, and the interactions between these building blocks. In addition, neutrinos must have played a role in the development of galaxies (and hence eventually stars and planets) and the continuing evolution of the cosmos, a role which may have been underestimated prior to the discovery of their mass.
Fundamental research has always been a long-term investment, and one which has continues to pay dividends in areas as diverse as medical imaging and treatment, micro-electronics, computing, and even the World Wide Web (invented at a physics laboratory in Europe).
Not at all. Super-Kamiokande is a multi-faceted detector with many capabilities. Additional data will allow more detailed tests of the mass and other properties of neutrinos. Search for signals of proton decay, magnetic monopoles, supernovae, and other neutrino sources outside the solar system complement the studies of atmospheric and solar neutrinos.
In addition, in 1999, a new experiment involving Super-Kamiokande - the "K2K" experiment - will begin. This experiment aims to further confirm the discovery of neutrino mass by directing a neutrino beam toward the detector from a particle accelerator 250 km away. These neutrinos should exhibit the same oscillation between neutrino types already observed for cosmic-ray and solar neutrinos. Using a detectors at the source of the neutrinos, and 250 km away, the changes in the neutrino beam can be precisely measured over a much greater distance than any previous experiment.
Super-Kamiokande is a collaboration of approximately 120 physicists from Japan, the United States, Poland, and the Republic of Korea. Roughly half its members come from Japan and half from the United States.
The cost of constructing the experiment was approximately $100M, the majority of which was provided by grants from the Japanese Ministry of Science. Significant funding was also provided by the United States Department of Energy, which continues to support the work of the American contingent.
An excellent, and highly accessible, introduction to particle physics is Gary Zukav's book The Dancing Wu-Li Masters.
The definitive treatise on solar neutrinos is John Bahcall's book Neutrino Astrophysics.
A more "cultural" (and humorous) look at the world of physics is Richard Feynman's book Surely You're Joking Mr. Feynman