Neutrinos barely have any mass at all, but in conclusive proof that all things are relative, some are hella fat while others are wicked thin. Since they're hard to measure, we have no idea which ones are which, but a fancy new neutrino detector in Minnesota will start solving the problem with the largest plastic structure ever built.
The deal with neutrinos is that they're available in three fun flavors: electron, muon, and tau. What's fun about these flavors is that they can switch back and forth between each other: if you start off with a bunch of tau neutrinos and then check back with them later, a bunch of them will have changed into muon neutrinos and electron neutrinos. Particle physicists have a fairly good idea about what the masses of each might be, but they're not sure which mass goes with which flavor.
To study neutrinos, you have to be able to catch them, and neutrinos are tricky little bastards to pin down. They're tiny, they're fast, and since they're electrically neutral they don't interact with any other sort of matter unless they smack right into it, which doesn't happen often. By the time you finish reading this sentence, about 450 billion neutrinos will have passed through every square centimeter of your body, and I'll bet you didn't feel a single one of them. The upside of this total lack of interest in just about everything is that neutrinos also don't care a jot about trivialities like hundreds of miles of solid earth and rock, meaning that you and generate them in one place (say, Fermilab in Illinois), and poke at them in another (say, Ash River, Minnesota).
The NuMI Off-Axis Neutrino Appearance experiment (called NOvA and don't ask me where they got the "v" from) is a brand new neutrino detector currently under construction in the wilds of Minnesota. Since neutrinos are so hard to stop, detectors have to be gigantic, and NOvA is no exception: when completed, it'll consist of 368,640 tubes of white PVC plastic glued together in a block that will measure 50 feet tall, 50 feet wide, and over 200 feet long. Each tube will be filled with a "scintillating fluid," and when a neutrino knocks into the fluid, it'll produce a tiny flash of light that will be measured and recorded and analyzed to figure out which flavor of neutrino it was.
The neutrinos themselves will generated at Fermilab and sent through 700 miles of solid Earth to NOvA in Minnesota up near the Canadian border. What's supposed to happen is that the neutrinos will change flavor along the way, from muon neutrinos to electron neutrinos. NOvA should be able to measure this, and use these observations to figure out which neutrino neutrinos have which mass.
Once NOvA is up and running in 2013, it should only take about six years of measurements to get some results back, so check back right here in 2019 for updates.*
*By 2019, DVICE will be manned exclusively by robots, Syfy will have further abbreviated itself to Sf, and Comcast will have purchased the United States government and sold it to Belgium.