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Yes - neutrinos have mass. Measuring them is a bit tricky and sometimes the experimental apparatus is non-trivial.
Backreaction notes the KATRIN experiment. (via Cosmic Variance) Moving the detector in this movie.
The detector was constructed in Deggendorf, 400 km from the experimental location of Karlsruhe ... but there was this detour...
The detector, by the way, is small in comparison to the detectors that surround the collision regions in the LHC (which gets beam this year!)
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