Neutrino versus Anti-neutrino Detection Is there a detection method in use that can distinguish a neutrino from its anti-neutrino?
 A: Some detection methods only detect neutrinos, as opposed to antineutrinos. For instance, the original solar neutrino experiment in the Homestake mine worked on the basis of the reaction
$$
\nu+{}^{37}{\rm Cl}\to {}^{37}{\rm Ar}+e^-
$$
if I recall correctly. Only a neutrino can induce that reaction; an antineutrino can't.
Other experiments can detect neutrinos through multiple channels, some of which (elastic scattering off an electron, for instance) are sensitive to both $\nu,\overline\nu$ and some of which only detect one.
A: Some more neutrino-antineutrino specific reactions:
$\nu_e n  \to  p^+ e^-$
$\overline\nu_e p^+  \to n e^+$
$\nu_\mu n  \to  p^+ \mu^-$
$\overline\nu_\mu p^+  \to n \mu^+$
A: Yes, as @voix shows in his partial list, neutrinos go either to $e^-$ or $\mu^-$ (or $\tau^-$) and antineutrinos go to the postive corresponding particles (conservation of lepton number).
In scattering experiments there may also be any number of hadrons produced depending on the energy of the beam.Because of weak interactions neutrino beams need trillions of neutrinos/antineutrinos impinging on the detector in order to see a reasonable number of neutrino/antineutrino interactions by the end of the experiment. Beams by construction are of one type of neutrino anyway, so it is a consistency check.
Experiments can assign interactions to neutrinos or antineutrinos depending on the charge of the outgoing lepton. The charges of the leptons are found from the curvature of the tracks in the magnetic field of the setup of the experiment.
The only way one can see if a neutrino or antineutrino is produced  in an interaction, is from the missing energy, because neutrinos/antineutrinos interact very weakly and cannot be detected within the apparatus. In events where all charged tracks have been measured one can also estimate the missing mass, and a neutrino/antineutrino is assigned by a fitting to a hypothesis  , if the missing mass is small.
A: The simplest thing to do is to look at the charge of the final state lepton, at least for a charged current interaction (exchange of a W). Negative-charge leptons result from neutrino interactions, and positive-sign leptons result from antineutrino interactions. This is because lepton number is conserved. At least it appears to be; there are some subtleties tied up with parity violation in the Weak interactions actually masking whether lepton number conservation is real or not. But for all current practical purposes, the final state lepton sign tells you what you need to know.
A: An additional means of distinction between the two is known as the Glashow resonance. The process occurs when a high energy ($E\sim6.3$ PeV) antielectron neutrino hits an electron at rest in the experiment and creates an on-shell $W^-$ boson. Since the earth (and pretty much everything we know) is only made up of matter and not antimatter, this process should only happen with antineutrinos.
The experimental status of this is that they haven't been seen but they probably should have been. IceCube at the south pole has seen neutrinos with energies up to $\sim2$ PeV. While the spectrum certainly falls with energy, the neutrino $+$ matter cross section increases significantly at the Glashow resonance, although only for $\bar\nu_e$. Currently there is some tension in this result. It is possible that high energy neutrinos disfavor antielectron neutrinos for some reason (there are several processes that lead to this result, but they don't seem to be that well motivated to me). Alternatively it could be that there simply aren't any neutrinos past $E_{\rm cut}$ for some value $2\lesssim(E_{\rm cut}/1{\rm\,PeV})\lesssim6.3$ (collaborators of mine have been working on descriptions involving both of these and I have been working on the latter). Of course both of these aren't well motivated and the most likely answer is either a combination of a downward fluctuation at the resonance and an upward fluctuation beneath it, or that IceCube has missed some systematics of their experiment.
