This is, of course, cancer. The most dangerous is then alpha radiation, followed by beta and last by gamma. However, since you must actually ingest the materials that emit alphas and betas, the most actually hazardous materials are those that emit gammas. Next to cancer, the most common image of the effects of radiation is the creation of mutations. Clearly radiation can cause damage to the DNA, but mutations require the damage to be subtle.
Massive damage leads to cell death.
The second protection, in humans at least, is that fertilized eggs which have significant damage simply do not develop. They are sloughed off and aborted spontaneously without anyone realizing it. In fact, some estimates suggest that almost half of the fertilized cells are lost in this natural process. If we focus on that damage that can disrupt the genetic machinery of the cell, i.e. the DNA, we must remember that in mammalian cells the nucleus of the cell is protected by a membrane at all times except during cell division. This membrane effectively reduces the effect of radiation damage in the cellular fluid as the poisons like hydrogen peroxide don't effectively penetrate.