The Lone Wanderer (Fallout Universe); via Rad Regeneration Perk
Ghouls (Fallout Universe)
Susan Murphy/Ginormica (Monsters vs. Aliens)
Spider-Man's (Marvel Comics) spider powers are all radiation-based.
Daredevil (Marvel Comics) originally gained his powers from exposure to radiation through a radioactive isotope that landed on his eyes.
Ninja Turtles (Teenage Mutant Ninja Turtles)
Due to the presence of Quantonium - a powerful alien radioactive energy - in her body, Susan Murphy (Monsters vs. Aliens) has grown in both strength and size, and eventually is able to control her size at will.
Conduits (inFamous) are not only immune to the negative effects of ray-field radiation, but larger concentrations of it can enhance and even activate conduit abilities.