What some are calling high levels of inorganic arsenic have been found in samples of rice and rice products (eg Rice Krispies and Geber's infant cereal) tested by Consumer Reports and the Illinois Attorney General's office. The FDA is conducting a larger study, but in preliminary results the agency says it has found roughly similar results.
Inorganic arsenic is a known carcinogen (bladder, lung, and skin cancers) when consumed in (cumulatively) large quantities. There are no standards yet for arsenic limits in foods, just for limits in water (there have been many cases in the past of cancers related to arsenic toxicity from drinking well water). The FDA says they will make recommendations after further study.
Brown rice tended to have larger quantities of arsenic than white rice.
Possible concern about inorganic arsenic levels in rice was discussed in an earlier thread, which mentioned this British report from 2007
Of course, the rice industry says this is all being blown way out of proportion and that it's nonsensical to single out rice as a problem food, since inorganic arsenic occurs in many foods and no one has shown that its presence in foods has caused health problems.