Is it dangerous if one elementary particle with high energy penetrates our brain? We might be killed if a bullet penetrates our brain. How about an elementary particle moving with high energy penetrates our brain? 
Assume that we can have exactly a single elementary particle for this imaginative experiment.
 A: 2012-07-11 Addendum
Based on excellent inputs, in particular from @annav, my answer is now "no, even a direct worst-case hit by the Oh-My-God particle would not kill you, even by radiation, because there is insufficient distance and angle to generate a fatal radiation cone. Thanks all, and be sure to look at the earlier answer that @dmckee pointed out.
** Original answer**
(My answer seems to differ from the earlier ones that @dmckee aptly pointed out, so I'll go ahead and risk posting it. My main difference is that I suspect that a head on collision with a large nucleus could produce a wide enough horizontal-splatter radiation cone to produce a fatal event.)
Since the 1991 Oh-My-God particle was most likely a proton and had the kinetic energy of a fast baseball, I'm going out on a limb and saying yes, you could be killed by a single particle. This Harvard physics site suggests an approximate energy transfer of about 0.2% in transfers with heavy nuclei, which as I discuss below may be enough to do you in with that kind of particle. But it would be the ensuing radiation event and cone that would do you in, not the kinetic energy of the particle.
The main issue is that your head doesn't have anything in it remotely solid enough to stop or even slow down a particle with that much momentum. So, like a locomotive passing through a cloud of fog, it's going to zip through pretty much as if your head isn't there.
The question, then, is to ask not what the fog will do to the locomotive, but what the locomotive will do to the fog -- that fog being your head.
Even a single solid, exactly head-on collision with a nice fat iron nucleus just as an ultra cosmic ray proton enters your head would probably not be a pretty event in terms of the resulting secondary radiation shower. I'm guessing (nothing more, I haven't tried to calculate anything) that outward splattering of a nice little quark plasma, one created as the iron nucleus vaporizes during the transition event, could produce a sufficiently wide cone of particle-zoo ejecta to irradiate a fatal percentage of your brain. Rapid heating of your brain would not be a problem, however, since 1/500 of the approximately 50 Joules of kinetic energy would work out to be only about 0.1 J of heat energy tops. By comparison a standard firecracker releases about 500 J of energy.
And what are the real odds on such a dead-center strike on a large nucleus near the surface of your brain, assuming you were an astronaut unprotected by out atmosphere? Low almost beyond belief. Look at the date on the Oh-My-God particle: 1991. We haven't seen one quite that feisty since. As @dmckee aptly notes, ordinary cosmic rays or their secondary outputs hit us all the time, and astronauts watch direct collision buzz through their retinas without much harm.
