Nuclear radiation isn't just a single phenomenon, and the effects differ between elements, depending on the kind of radioactive decay they undergo and the parts of the body in which they concentrate.
Often three things fall under the catch-all term radiation: gamma rays, which are high energy photons (light), beta particles, which are electrons and positrons, alpha particles, which are helium nuclei, and neutrons.
Generally speaking, gamma radiation is dangerous at high doses but can be blocked by good shielding. Neutrons can be slowed down and stopped by shielding as well, usually an element that absorbs them such as cadmium or a material like water. Alpha particles don't penetrate the skin, but can be ingested or inhaled.
What follows is a quick guide to which elements are most common (and of most concern).