Many parts of DC are safe beyond the areas I will list here, but why chance it if you don't know where you are?
If you are on the subway stay on the Red line between Union Station and Shady Grove, Maryland. If you are on the Blue or Orange line do not go past Eastern Market (Capitol Hill) toward the Potomac Avenue stop and beyond; stay in NW DC and points in Virginia. Do not use the Green line or the Yellow line. These rules are even more important at night. There is of course nothing wrong with many other areas; but you don't know where you are, so you should not explore them.
What a great look into the movement this guide to D.C. is. "Not being curious due to crippling, ignorant fear" is actually a pretty good description of Glenn Beck fans in general. You should read the whole post, which include first-person accounts of the terrors of Washington, which are deemed to be "more dangerous than Baghdad." I'm sad to admit this how-to guide originated with the Maine Tea Party, who continue to make residents of my home state look like idiots.