Although I was lucky enough to tour Brookhaven's RHIC accelerator during a period of scheduled downtime, my trips to the LHC and Fermilab both took place while the particle accelerators were in operation. Given the tremendous energies involved, it meant that it was simply not safe to go anywhere near the active hardware, since that's a sure way to pick up a healthy dose of ionizing radiation. But Fermilab had an exception to that, a place where it wasn't just acceptable to look at working hardware, but it was actually possible to walk right through a particle beamline. The secret? The particles were neutrinos.
Neutrinos are uncharged particles and are so light that, for decades, most physicists assumed they were actually massless. As if that weren't enough, they only interact with other matter via the weak force, which is only significant at short distances. Thus, for the most part, they generally pass through matter without incident—trillions go through your body every minute, but most of us will only have them hit anything a total of about three times in our entire lives.
They are so disinterested in interacting with matter that Fermilab is able to create a beam of neutrinos and direct them to a mine in Minnesota without losing enough of them on the way to interfere with the experiment.