Dr. Michael Greger, of Nutritionfacts.org fame, recently posted a series of videos about levels of arsenic in rice. My takeaways:
1) rice from California & Asia has lower arsenic (avoid rice from southern states of USA)
2) when cooking, boil rice like pasta & drain excess water*
3) vary the grains you eat
* I follow Jeff Novick's fool-proof cooking method: In an uncovered pot with generous amount of water, boil brown rice for 30 minutes. Drain it. Place rice back in pot, covered & off of stove burner, for 10 minutes. (I love the popcorn-like smell of cooking rice!)