I come from a part of the world (interior Alaska) where the natural background levels of arsenic in groundwater (well water) and surface water (streams and rivers) are higher than the EPA standards for drinking water -- sometimes much
higher. This gives municipal water treatment utilities absolute fits in Alaska's few towns large enough to provide public water; it also means it can be technically illegal to fill a
bucket from your kitchen sink tap and then dump that bucket into the stream at the bottom of your
yard -- because your drinking water is technically a pollutant, even though there might be less arsenic in it than there is in the natural background of the stream you're dumping it into.
So, basically everybody I ever knew spent their entire lives drinking arsenic-laced drinking water, and yet there's little notion (based on epidemiological studies or any other medical observation) of actual health problems ever having been suffered from Alaskan drinking water. Like most potential toxins, with arsenic the dose matters. And the regulatory standards are conservative. EPA acknowledges no safe level of the stuff, which basically means they are using a homeopathic standard: they believe, or at least they fear, that even a single atom (or molecule of an arsenical compound) can have a toxic (or more likely carcinogenic) effect. How likely you think that is to be true is a personal risk-management decision; science cannot currently answer it for you.
How do arsenic levels in rice compare with the natural-background levels of arsenic in interior Alaska? There's probably no rigorous scientific way to even phrase that question, much less answer it. However,
Consumer Reports says they found rice with enough arsenic in it that one serving of rice contained as much arsenic as the water you would drink in a day and a half at EPA's drinking water standard. So eating rice once every day and a half is roughly comparable to using tap water as your sole drinking water source -- or at least that's how I parse the risks.
There's an interesting document
here that may help you parse the risks. It's from the water department in Anchorage, Alaska, and it's talking about an area where
local residents have drinking water
wells averaging 89 ppb (parts per billion) of arsenic. It tries to answer the question of whether that level (which is nine times the 10 ppb level that EPA allows in drinking water) is harmful to human health. And it's clear that they don't know
the answer. Instead what they do is reference the only documented long-term medical effects of arsenical drinking water that they have (from Taiwan and South America) where drinking water levels are said to be "higher" than the 89 ppb in question. But they do not say
how much higher. (I think I remember seeing that research back when I was working on this stuff professionally, and I am remembering hundreds or thousands of ppb. But I could
so easily be wrong.) Thus, if we sort of round things to single significant digits and summarize things implied but not stated, the bottom line is that eating rice every day is in the same order of magnitude of risk as drinking tap water. And we've got populations in Anchorage whose water is roughly ten times worse than the EPA standard (which would make it in the same order of magnitude as eating ten services of rice a day) and no evidence that they came to any harm. But we know that if we go up another order of magnitude in drinking water, then they can document a bunch of cancers from it. So it's pretty clearly a bad idea to eat fifty or a hundred servings of rice a day.
Further complicating all of this is the number of different chemical compounds that arsenic forms. Each one of them has a different bioavailability, and probably thus a different degree of uptake in plants. What's more, toxicity and carcinogenicity is not well-documented for each distinct arsenical compound. So there's no real way to know if the arsenic in your rice (or your drinking water) is one of the bad ones or one of the less-bad ones. I tend to have a bias toward the notion that the compounds that get cycled through plant systems are less likely to be harmful than the ones plants won't touch, but I freely admit this is most likely a superstitious notion on my part.
Very long winded way of saying: "No, I don't worry about arsenic in my rice." I don't wash my rice. I also don't throw out any pot liquors. I don't much enjoy greens, but the ones I do eat go into soups and stews, so nothing gets washed or leached away in the cooking process.