You probably should. Believe it or not, most rice has arsenic. Rice absorbs more arsenic from the soil and water than other grains do. A Consumer Reports tests showed about 1 microgram to 7 micrograms arsenic in 1/4 cup uncooked white rice (and even more for brown rice). According to Nutrition Action Health Letter (March 2013), most Americans are exposed to lower levels of arsenic than in other countries, but it's best to play it on the safe side, since arsenic is a carcinogen.
Because of my limited diet, I do eat white rice weekly, so I decided to start rinsing my rice and cooking it in a large amount of water and then draining the extra water off when tender (just like cooking pasta). This can remove up to half the amount of arsenic that may be present according to Nutrition Action. I found that the rice cooks quicker too, only taking about 12 minutes.
To rinse my rice, I put it in a fine mesh sieve and take my sink's sprayer to hose it down. I give it a really good rinse and toss it around a lot.Then I fill a large cooking pot with water and boil the rice for about 12 minutes, then drain. Just like cooking pasta!