The practice of rinsing rice started primarily because talc or glucose had been added to the rice, ostensibly to preserve the rice and to prevent the grains from sticking together before it was cooked -- i.e., during processing, shipping, and storage.
However, talc hasn't been added to American- or European-produced rice for decades -- it's banned in this and many other countries because it's a health hazard as the talc may contain asbestos and has been linked to stomach cancer.
According to The New Food Lover's Companion, "Talc-coated rice is white rice that has a coating of talc and glucose, giving it a glossy appearance. The coating acts as a preservative and the practice was once widely used to protect rice during long sea voyages. Today coated rice (clearly labeled as such) is available only in a few markets, usually those specializing in South American foods. It must be thoroughly rinsed before cooking, as the talc can be contaminated with asbestos."
IMHO, there's really not much reason to rinse rice that hasn't been coated with talc or glucose. I never bother to rinse domestically produced rice. However, I do carefully wash anything from foreign sources, such as the Indian and Thai rices I buy at Trader Joe's, but only out of health concerns and to remove any impurities. (I prefer rice that is somewhat sticky in the Japanese style, such as Calrose -- I've never understood the preference for individual grains of cooked rice as it tastes no better and is harder to eat with a fork or chopsticks.)
Moreover, in some instances rinsing can remove nutrients. White rice is pretty much nothing but carbohydrates as the nutrients are in the outer brown husk that's removed to make the rice white. White rice is often "enriched" by the addition of vitamins and minerals to replace those missing nutrients. Wikipedia notes that "While the cheapest method of enriching involves adding a powdered blend of nutrients that will easily wash off (in the United States, rice which has been so treated requires a label warning against rinsing), more sophisticated methods apply nutrients directly to the grain, coating the grain with a water insoluble substance which is resistant to washing."
So whether to rinse or not boils down to the type of rice you have, where it came from, and whether you care about having individual grains of rice on your plate.