It's been said that cockroaches are resistant to radiation and might be the largest surviving animal following a nuclear onslaught. I've been wondering whether there are Darwinian factors that might have selected this, noting that cockroaches are both "old", and fairly simple creatures.
Being old, the cockroach may date from a long-past period during which naturally-occurring radiation bursts may have been a selection factor. For example, if water washes through a reef of fissionable material, it could slowly concentrate this material to a critical mass that would not explode like a nuclear bomb, but could cause a plume of radioactivity similar to a nuclear reactor mishap. Animals that could sense radiation and move away, and/or have better-shielded or more structurally-robust genetic material, might be selected in for survival in such environments.
More robust genetic material also means less mutability, which disfavors complexity and would tend to cause the organism to remain genetically unchanged over the ages, as may be the case with the cockroach.
Even if such circumstances did not occur on this planet, you could postulate a planet on which they did. A planet rich in fissionable materials would probably also be rich in heavy elements suitable for shielding, so a radiation-aware organism might not only flee the radiation it senses, but could also seek, create or incorporate appropriate shelter. You could also postulate organisms that might derive their energy needs from controlled exposure to the fission process.
Animals with radiation awareness could be useful things to have around :-)