We were actually on vacation in DC at the time... were going to go to the Pentagon that day, but at the last moment, changed plans to go to the Baltimore Aquarium. We got to the aquarium just as it was opening.
After it had begun, the aquarium closed with a few people (including us and a security guard who didn't have the keys to get everyone -- including himself -- out) still locked in it, and I remember sitting there, waiting, wondering so... what now? No-one really quite comprehended what was going on. Pearl Harbor was, like SoP said, one of the first things that came to mind. Worse than Pearl Harbor. Eventually, someone someone finally came at let us out, helped sort out what rumors were true -- as far as anyone could tell at that point.
We spent the rest of the day driving around, trying to figure out how to get back to where we were staying, with some relatives.
Two days later, we ended up going back into DC proper. Whereas before, everything was active and busy, people now seemed subdued. Every time a fighter or other military aircraft would go overhead, everyone (including us) would stop, freeze up, and stare up at the sky.
The sight of the Air Force soaring above was, in some ways comforting, but it was a rather horrifying reminder as a sudden silence would descend over everyone, broken only by the horrifying sound of some aircraft.
Then we got on the metro. As we got off one of the trains, and were walking up toward the exit, there was a bomb scare on the train we had just been on.
But I remember that the evening of the 11th, there was a truck, full of people, who had already begun driving around, blaring the patriotic music and singing outside a Wendy's on our winding route back to where we were staying.
Anyway, that's my spiel. I know other people probably have more significant stories than mine, but there it is, for what it's worth.