Like most, was at work and probably would have had no inkling that anything was going on, but one of my colleagues was on the phone to his GF who was watching Sky News at home and she happened to mention that there had been some sort of incident at the World Trade Centre, so I was getting half the story relayed to me. First reports had it as a small explosion, then that maybe that a light aircraft had hit the building (presenters presuming it was a terrible accident), then just as they started to confirm that it was actually a jumbo jet, the second one hit and all of a sudden you realised this was no longer an accident.
Only about three months before had we rolled out internet access to every PC in the office (previously only a limited number of machines had it) and it was still considered a bit of a novelty at that point and most people couldn't see the point, but for the rest of the afternoon pretty much everyone was glued to it to find out what the latest news was and obviously it completely ground to a halt. Though I'm not sure whether that was just the connection in our office, or whether everyone in the world was trying to access the more popular sites and they couldn't cope with the traffic. I did notice that by using sites that were in parts of the world that would have been asleep (e.g. the Australian mirror of the CNN website), you were able to connect a lot quicker than to sources from Europe or America, so it is quite possible that was the case.
Literally no work got done for the rest of the day - people were just too shellshocked.