With low levels of radiation, it's different for everyone. Without going too in-depth into Biochemistry, DNA has the ability to repair itself from damage such as radiation damage. In a perfect world, these mechanisms would always work. The problem is when they don't work and radiation alters genes that are crucial for the appearance of cancer. With higher levels of radiation, energy directly damages cells. Some cells are more prone to damage than other cells, but this is a topic concerning only the Japanese and people who work in nuclear reactors. If we strictly want to put a number on dangerous radiation, I'd say about 100 times above normal is already slightly threatening.