Is there any risk of illness from eating rice?

Yes. Uncooked white rice frequently contains inactive bacteria known as  Bacillus cereus. These bacteria can form protective spores that survive the cooking process. If the rice is cooled slowly, these spores can germinate, grow, and produce an emetic--or vomit-inducing--toxin. Reheating rice before serving it will not inactivate the toxin nor kill all bacterial cells. Therefore, either keep cooked rice  hot or cool the rice as quickly as possible. In general, proper storage, handling and preparation of cooked rice eliminate most risk of illness.
 
Uncooked brown  rice also may present problems. Since brown rice features an oil-rich germ, it is more susceptible to becoming rancid than white rice. Refrigerating the rice in an airtight container will delay the onset of rancidity. White rice, by comparison, will keep almost indefinitely in dry, cool environments.
 
Source(s):
whfoods.com "Brown Rice"
New Zealand Food Safety Authority "Safe Cooling of Cooked Rice"