It depends. Although at first it can be answered with a "yes, absolutely", i'd like to record that our body is traversed daily and continuously by particles of all kinds. An example of this is the Sun, which is an inexhaustible source of subatomic particles such as neutrino. These particles also come from the remains of the big bang and certain reactions that occur in the Earth's atmosphere but don't worry, nothing happens because these particles pass through us, they're not highly energetic.
From this we could infer that not all particles are the same and that their dangerousness depends on the type and the energy they have. Highly energized particles are able to break down molecules such as the DNA into our cells and cause cancer.
Answering the initial question, if we were going through a beam of proton particles, for example in the LHC, it wouldn't be good for our health due to the high energy that would be released.
An example of this was given on July 13, 1978 when the Russian physicist Anatoli Bugorski was traversed by a proton beam that came from a particle accelerator near Moscow. The physicist was that day checking a small accelerator failure and safety measures failed. Anatoli leaned over the accelerator and stepped in the path of the proton beam that was spouting at that moment.
The Russian physicist said he had seen a flash more intense than thousands of suns, but hadn't felt pain. In the days after the accident Anatoli Bugorski noticed that the left side of his face was swollen, his face skin also began to peel and the path that the proton beam had followed in its path could be observed.
It seems that the proton beam burned off portions of bone and brain tissue and, although he was expected to die, he didn't. Anatoli lost his left ear hearing but was able to continue working and studying. The affected area of his face was paralyzed, occasionally Anatoli suffers from epileptic seizures but remains in relatively good health.
