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I think washing is unnecessary unless your rice is dirty for some reason (some rice can be dusty, though in western countries I think this is rare).
If I need to have rice that sticks together, I'll use the traditional absorption method: about 2 parts water to 1 part rice, cook in under a lid for 20-30 minutes. No need to wash the rice as its supposed to have that starch for stickiness.
If I need to have rice that stays separate (for fried rice for example), I'll use the pasta method and boil the rice in a large amount of water, then pour through a strainer. Again no need to wash, as cooking in lots of water does essentially the same thing and the excess starch is poured off with the water.