The latest reactor neutrino data from a MINOS pre-publication favors at least three generations of ordinary neutrinos (Lubos felicitously calls them "fertile neutrinos"), but while not ruling them out, places significant empirical bounds on a fourth generation sterile neutrino.
The new MINOS study doesn't favor more than three neutrinos types as strongly as a couple of previous neutrino studies in 2010 (MiniBooNE) and 2011 (also here, summarizing data from multiple experiments)(with both four and five generations within the realm of consistency with experimental results for reactor experiments and a three generation scenario disfavored; evidence from astronomy data in favor of more than three generations was also announced at the Neutel Conference in 2011 (link not easily at hand)).
As I have previously noted at this blog, precision electroweak data strongly support the existence of at least three neutrino generations and strongly disfavor the existence of any additional neutrinos with a mass of less than 45 GeV (half of the Z boson mass), that interact via the weak force, hence the presumption that any additional light neutrino types must be "sterile" (i.e. right handed particles that don't interact with the weak force and hence evade detection via weak force interactions such as W boson and Z boson decays). This is 10^3 orders of magnitude higher than the upper bounds on tau neutrino mass, and perhaps much more, as there are upper bounds on the tau neutrino mass, but not a very firm mean absolute value of it and other consideration (estimates of the mass difference between the three neutrino mass eigenstates in a three eigenstate model) suggest a tau neutrino mass much, much lower than the 15.5 MeV upper bound cited above.
The best experimental estimate (as of 2010) of the square of the mass difference between the first and third neutrino mass eigenvalue is 2.5 × 10^−3eV^2, while the square of the mass difference between the first and the second is estimated at 7.6 × 10^−5eV^2. Unless different generations of neutrino mass eigenvalues have huge masses relative to the difference in masses between the three mass eigenvalues, the absolute values should be within an order of magnitude or two of the square root of the values above, implying a tau neutrino mass on the order of 0.05 eV, and probably not larger than the single digit eV range (and a muon neutrino mass on the order of 0.008 eV and probably not more than a fraction of an electron volt, with the electron neutrino being even lighter). This would imply that any fourth generation fertile neutrino would have to be 10^10 times as heavy as a tau neutrino, when the mass gaps between neutrino mass eigenvalues would seem to be consistent with a 10^2 gap between the third state and the second (similar to the high end of the mass ratios between some of the other pairs in the Standard Model fermion mass matrix), and a gap on the order of less than a power of ten between the second state and the first one. For comparison purposes, fourth generation quarks or charged leptons with masses in the single digit TeV range would not present a major departure from the patterns seen in the first and second generations of Standard Model fermion masses.
In contrast, the largest order of magnitude jump between any two particles of the same type of successive generations observed to date is on the order of 10^2 orders of magnitude higher than the next lighter particle of the same type. We don't have any really solid way to make predictions about the mass of a hypothetical fourth generation "fertile" neutrino, but we also haven't identified any pattern in the mass matrix data that we have that could explain that kind of phenomenal leap in mass from a third generation to a fourth generation fertile neutrino.
Certainly, the signs of fourth or fifth generation neutrinos reported in 2010 and 2011 don't show indications of a neutrino of those types having masses in excess of 45 GeV, as energetic limitations would greatly suppress oscillations of lighter neutrinos to these generations in reactor and atmospheric measurements - only collider experiments generate a significant enough number of neutrinos at those energies to lead to the predictions of fourth or fifth generation neutrino mass states that we have seen in both reactor and atmospheric studies.
Of course, as I noted in a post at this blog earlier this month, any composite particles made out of neutrinos would also not be forbidden by precision electroweak measurements.
The notion of a new fundamental sterile neutrino particle has not been viewed as particularly radical by many particle physicists because of (1) the absence of right handed neutrinos that are ordinary particles (as opposed to antiparticles) in the Standard Model, unlike all other Standard Model fermions, (2) the attractiveness of sterile neutrinos as a possible means of explaining Majorana neutrino mass in the Standard Model and (3) the attractiveness of sterile neutrinos as a dark matter candidate. So these possible sterile neutrino discoveries have not resulted in the backlash that possible superluminal neutrino data from the OPERA experiment has produced. Adding right handed neutrinos to the Standard Model is generally viewed by physicists as a very modest extension of the Standard Model that does not deeply disturb the larger framework of Standard Model physics. Fourth generation "fertile" neutrinos are also, due to their presumably light masses relative to other hypothetical fourth generation versions of Standard Model particles, a likely first fourth generation Standard Model extension particle to be discovered experimentally.
If experiments show that there aren't any sterile neutrinos or fourth generation "fertile neutrinos", however, the problem of a lack of an experimentally supported dark matter candidate in particle physics only grows more vexing, and the naiive SM4 extension of the Standard Model with four rather than three generations of Standard Model particles also grows increasingly disfavored.
Indeed, many atmospheric neutrino detectors should be capable of direct detection of some lighter dark matter candidates, even if they aren't actually a neutrino type. For example, many of these experiments could detect hypothetical lightest supersymmetric particles although they might look like highly energetic and/or massive neutrinos rather than another kind of particle to the detector. So, tightening experimental boundaries on sterile neutrinos also tighten the parameter space for potential dark matter candidates and for SUSY (and by extension for string theory). Given that observations related to galactric scale and larger structure and galaxy type frequency from astronomy are placing independent boundaries on dark matter candidates by a different methodology. Specifically, this data seems to disfavor dark matter candidates with GeV or heavier masses in favor of dark matter candidates with masses on the order of a keV. (The astronomy of large scale structure also disfavors dark mater candidates in the eV or less mass range). Thus, experimental evidence seems to be leading to an overconstrained parameter space for dark matter in which no dark matter candidates are consistent with the data (a conclusion that, if reached, would suggest that dark matter effects may actually be a function of a flaw in the equation for gravity in General Relativity or a failure to draw conclusions from those equations properly).
Similarly, experiments that set out to detect cold dark matter with GeV masses also disfavor the existence of fourth generation or higher neutrinos (fertile or sterile) with GeV scale or larger masses.