Boy, this thread certainly isn't destined to go badly.
Well, as for me I was in college at the time. I had late morning classes (11 AM), so I was up listening to the radio and playing games. Same old, same old. Then over the radio there's a sketchy announcement of a small plane (the reporters were very unsure of the details at the time) hitting the World Trade Center, and there was speculation that something might have gone wrong with a private plane. Then the second one hits, and the truth becomes gradually clear.
Naturally, my classes were canceled for the day, and my mother asked me to go pick up my sister from our local high school. High Schools being ridiculously full of bureaucracy, they made me wait until the entire school was released for the day. At least I only had to wait a good half hour or so.
And yeah, that was kind of all the non-political stuff that happened that day. Aside from a major occurrence of mass murder, it was a pretty typical day.
I continued to listen to the radio while playing...something. It was September 2001, so it was very likely something GameCube and adventure-y, but I don't remember what.
Later in the day, I went in to work at my local drugstore, and as you might expect there was a sudden mad dash by people to purchase anything with an American flag on it. We had the radio going all night, and people were pretty tense, but it was otherwise an ordinary night at work.